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WIRELESS  TELEGRAPHY 


BY 
DR.  J.  ^ENNECK, 

PROFESSOR  OF  PHYSICS  AT  THE  TECHNICAL  HIGH  SCHOOL  OF  MUNICH. 


TRANSLATED  FROM  THE  GERMAN 
BY 

A.  E.  SEELIG,  E.  E. 


FIRST  EDITION 
FIFTH  IMPRESSION 


McGRAW-HILL  BOOK  COMPANY,  INC, 

239  WEST  39TH  STREET.    NEW  YORK 


LONDON:  HILL  PUBLISHING  CO.,  LTD. 

6  &  8  BOUVERIE  ST.,  E.  C. 

1915 


COPYRIGHT,  1915,  BY  THE 
McGRAw-HiLL  BOOK  COMPANY,  INC. 


First  printing,  August,  1915 
Second  printing.  May,  1916 
Third  printing,  July,  1917 
Fourth  printing,  January,  1918 
Fifth  printing,  March,  1918 


.    •  ; 

• '•'   93 


THE  MAPLE  PRESS  YORK  F  JL 


Y/ 


EXTRACT  FROM  AUTHOR'S  PREFACE  TO  THE 
FIRST  EDITION 

This  book  was  written  at  the  suggestion  of  the  publisher,  Dr.  Enke. 
It  was  originally  intended  to  be  an  abridged  form  of  my  larger  book 
" Elektrornagnetische  Schwingungen  und  drahtlose  Telegraphic"  (Stutt- 
gart, 1905).  It  has,  however,  developed  into  something  quite  different; 
evidence  of  this  lies  in  the  fact  that  only  79  of  the  332  illustrations  of  the 
larger  book  have  been  reproduced  here. 

Since  I  began  writing  this  book  (winter  1905-1906)  conditions  in  wire- 
less telegraphy  have  changed  greatly.  The  mere  fact  that  new  devices 
and  methods  have  appeared  would  be  of  relatively  little  importance; 
but  the  points  of  view  determining  the  consideration  of  many  of  the 
problems  of  the  art  have  changed  entirely.  This  necessitated  rewriting 
many  portions  of  the  book,  which  would  otherwise  have  been  out  of  date 
from  its  very  publication.  I  need  hardly  dwell  on  what  this  has  meant 
for  both  the  publisher  and  myself. 

The  mathematical  premises  are  the  same  as  in  my  larger  book.  In 
the  text,  knowledge  of  only  elementary  mathematics — the  use  of  differ- 
ential and  integral  calculus  would  have  offered  no  advantage, — in  the 
Notes,  knowledge  of  the  electromagnetic  theory  is  assumed.  The  phys- 
ical premises  are  somewhat  higher  than  in  the  larger  book ;  knowledge  of 
experimental  electro-physics  and  of  the  phenomena  of  alternating  cur- 
rents, in  short  the  ground  covered  by  the  first  four  chapters  of  my  larger 
book,  is  necessary  for  a  thorough  understanding  of  this  volume. 

I  have  been  somewhat  more  sparing  with  the  bibliography,  for  since 
a  year  ago,  Dr.  G.  Eichhorn,  in  the  "  Jahrbuch  fur  drahtlose  Telegraphic, " 
gives  detailed  references  to  the  literature  on  the  subject. 

As  regards  the  commercial  form  of  the  apparatus,  most  frequent  refer- 
ence has  been  made  to  the  German  manufacturers  (Ges.  f.  drahtl.  Tel. 
and  Amalgamated  Radio-telegraph  Co.,  i.e.,  C.  Lorenz,  A.  G.).  In  so 
doing  I  had  no  desire  to  show  these  firms  any  preference.  Description 
of  all  the  different  makes  of  apparatus  would  have  been  prohibitive,  and 
I  have  simply  chosen  as  examples  the  apparatus  of  those  firms  which 
placed  exact  data  and  photographs  at  my  disposal.  Moreover  other 
makes  of  apparatus  are  fully  described  in  other  books;  I  might  mention 
the  excellent  works  of  J.  A.  Fleming  and  particularly  of  J.  Erskine- 
Murray  in  this  connection. 

J.  ZENNECK. 

BRAUNSCHWEIG,  PHYSIKALISCHES  INSTITUT 

DER  TECHNISCHEN  HOCHSCHULE, 

Dez.,  1908. 

V 

373881 


AUTHOR'S  PREFACE  TO  THE  SECOND  EDITION 

Only  two  and  a  half  years  after  the  appearance  of  the  first  edition, 
a  second  one  has  become  necessary,  even  though  a  French  edition  had 
already  appeared  in  the  meantime.  The  book,  therefore,  has  been  ac- 
corded a  much  more  favorable  reception  than  I  had  dared  hope. 

This  served  particularly  to  spur  me  on  to  do  everything  within  my 
power  to  make  the  second  edition  representative  of  the  present  status  of 
wireless  telegraphy.  Due  to  its  rapid  development,  this  meant  an  ex- 
tensive revision  of  the  entire  book. 

Unfortunately  I  found  it  impossible  to  carry  out  this  revision  without 
extending  the  scope.  In  view  of  this  wider  scope,  the  book  has  been 
renamed  " Textbook"  ("Lehrbuch")  instead  of  " Elements"  (" Leitfaden") 
"of  Wireless  Telegraphy." 

In  choosing  my  subject  matter,  I  was  guided  chiefly  by  the  standpoint 
of  the  physicist.  I  have  frequently  discussed  arrangements  or  devices 
involving  a  new  physical  idea,  even  though  knowing  that  they  had 
either  not  been  used  to  date  or  are  no  longer  used  in  practice.  To 
confine  ourselves  to  what  is  of  practical  importance  will  only  be  proper 
when  once  it  has  been  fixed  what  really  is  of  "  practical  importance." 
On  this  point,  however,  the  views  of  experts  have  changed  very  rapidly 
during  recent  years;  even  to-day  individual  views  diverge  widely  and 
seem  to  be  influenced  less  by  scientific  reasons  than  by  patent  rights. 

Unquestionably,  theoretical  investigation,  laboratory  experiments  and 
experiences  in  practice  have  cleared  much  in  recent  years.  Nevertheless, 
there  still  remain  a  number  of  problems  which  find  no  answer  in  the  re- 
sults obtained  to  date.  If  then  my  presentation  of  these  problems  falls 
short  of  the  necessary  clearness,  the  fault  does  not  rest  entirely  with  me. 

In  this  edition,  as  in  the  first,  I  have  received  friendly  cooperation 
from  many  sources:  from  Dr.  L.  W.  Austin  (Washington,  D.  C.),  H.  Boas 
(Berlin),  Dr.  L.  Cohen  (Brant  Rock),  F.  Ducretet  and  E.  Roger  (Paris), 
Dr.  Erskine-Murray  (London) ,  the  Gesellschaf t  f iir  drahtlose  Telegraphic 
(Telefunken  Co.,  Berlin),  Dr.  E.  Huth  (Berlin),  the  C.  Lorenz  Co. 
(Berlin),  the  Marconi  Wireless  Telegraph  Co.  (London),  Dr.  E.  Nesper 
(Berlin),  Dr.  E.  H.  Riegger  and  Dr.  Rukop  (Danzig),  Dr.  G.  Seibt 
(Berlin),  the  Societe  frangaise  de  radioelectrique  (Paris),  and  Prof.  C. 
Tissot  (Brest).  To  all  these  I  herewith  express  my  thanks. 

vii 


viii  AUTHOR'S  PREFACE  TO  THE  SECOND  EDITION 

Particular  thanks  are  due  Dr.  A.  Meissner  (Berlin),  Prof.  Vollmer 
(Jena),  and  Prof.  M.  Wien  (Jena).  These  have  gone  to  the  great  trouble 
of  reading  through  the  entire  proof,  and  by  their  valuable  advice  have 
guarded  me  against  many  errors  and  defects. 

Lastly,  I  thank  the  publisher,  Dr.  A.  Enke  (Stuttgart)  for  the  kind 
interest  he  has  evidenced  in  the  preparation  of  the  book  in  its  final  form. 

J.  ZENNECK. 

DANZIG-LANGFUHR,  PHYSIKALISCHES  INSTITUT 
DER  TECHNISCHEN  HOCHSCHULE, 
Nov.,  1912. 


TRANSLATOR'S  INTRODUCTORY  NOTE 

Few  students  of  wireless  telegraphy  need  to  be  introduced  to  "Zen- 
neck."  To  many,  however,  this  splendid  work  has  remained  a  "  closed 
book"  due  to  lack  of  knowledge  of  the  author's  language.  Hence  this 
translation — in  the  hope  that  it  will  fill  a  real  need. 

Aside  from  the  comprehensiveness  of  the  work  as  a  text-book,  the 
author,  without  failing  to  give  full  credit  to  the  best  that  has  been  done 
in  America,  naturally  pays  most  attention  to  the  work  done  in  Europe, 
especially  in  Germany,  and  thus  gives  us  an  insight  into  the  excellent 
results  accomplished  abroad  by  inventors  and  engineers  in  developing 
the  art  based  on  Marconi's  fundamental  invention. 

Rather  than  take  the  risk  of  distorting  the  author's  precise  meaning, 
the  translator  has  at  times  retained  a  very  literal  translation  in  preference 
to  adopting  the  customary  English  phraseology.  Moreover,  when 
tempted  to  add  something  to  or  modify  the  original  (as  for  instance  in 
connection  with  recent  "high  frequency"  apparatus),  the  translator 
finally  decided  to  let  Zenneck  be  Zenneck. 

A  word  of  thanks  is  due  to  Dr.  L.  W.  Austin  for  occasional  friendly 
assistance,  as  well  as  to  the  publishers  for  their  cooperation  in  the 
preparation  of  the  book. 

A.  E.  SEELIG. 

WELLSVILLE,  N.  Y., 
August,  1915. 


CONTENTS 

CHAPTER  1 

THE  NATURAL  OSCILLATIONS  OP  CONDENSER  CIRCUITS 

PAGE 

1.  Oscillations  Produced  by  Charging  the  Condenser 1 

§1.   The  Frequency 

2.  Experimental  Determination  of  the  Frequency 3 

3.  Calculation  of  Frequency  (Thomson's  Equation) .    .  6 

4.  Condensers  in  Series  and  in  Parallel 7 

5.  The  Practical  Importance  of  Thomson's  Equation 9 

§2.   The  Damping 

6.  The  Transfer  of  Energy 9 

7.  The  Various  Causes  of  Damping 11 

8.  Condenser  Circuit  without  Spark  Gap.     Damping  Due  to  Heat  Loss .  11 

9.  Condenser  Circuit  with  Spark  Gap.     Damping  Due  to  Spark ....  13 

10.  Methods  for  Determining  the  Spark  Gap  Damping 16 

11.  The  Factors  Which  Determine  the  Amount  of  Gap  Damping  ....  16 

12.  Spark  Gaps  in  Series  (Multiple  Gaps) 20 

13.  Energy  Losses  in  the  Dielectric  of  the  Condensers 20 

14.  Energy  Lost  by  Leakage  Discharge 21 

15.  Energy  Lost  by  Eddy  Currents 22 

16.  Relative  Importance  of  the  Various  Energy  Losses 23 

CHAPTER  11 
OPEN  OSCILLATORS 

§1.   The  Lineal  Oscillator 

17.  The  Fundamental  and  Upper  Harmonic  Oscillations 24 

18.  Current  and  Potential  Distribution  in  the  Fundamental  Oscillation.  .  24 

19.  Frequency  of  the  Fundamental  Oscillation 26 

20.  The  Electromagnetic  Field  of  the  Fundamental  Oscillation 27 

21.  Damping  of  the  Fundamental  Oscillation 31 

22.  Upper  Harmonics  of  the  Lineal  Oscillator 32 

23.  Coils 33 

§2.  General  Properties  of  Open  Oscillators 

24.  Current  and  Potential  Distribution  along  a  Wire 34 

25.  The  Electromagnetic  Field  at  Great  Distances  from  the  Oscillator.    .  35 

26.  The  Radiation  of  an  Oscillator 39 

27.  Effective  Capacity  and  Effective  Self-inductance  of  an  Oscillator   .    .  40 
§3.   Various  Forms  of  Complex  Oscillators 

28.  Lineal  Oscillator  with  Two  Equal  Capacities,   One  at  Each  End 
(Hertz  Oscillator) 41 

29.  Lineal  Oscillator  with  Capacity  at  One  End 42 

30.  Lineal  Oscillator  Containing  Series  Condensers 43 

31.  Lineal  Oscillator  Containing  Series  Inductance 44 

32.  Lineal  Oscillator  with  Both  Inductance  and  Capacity 45 

33.  Grounded  Oscillators : 46 

xi 


xii  CONTENTS 

CHAPTER  111 
THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT 

PAGE 
§1.  Resistance,  Self-induction  and  Capacity 

34.  Current  Distribution  in  Cross-section  of  Solid  Wires 47 

35.  Coefficient  of  Self-induction 47 

36.  Resistance  of  Straight  Wires 48 

37.  Resistance  of  Coils 50 

38.  Coils  Having  Variable  Self-induction 51 

39.  Condensers  of  Constant  Capacity 54 

40.  Variable  Condensers 59 

§2.  Current  and  Voltage 

41.  Relations  between  Current  and  Voltage  Amplitudes 62 

42.  The  Break-down  Voltage  and  Gap  Length   . 64 

43*  Insulation  of  Conductors 66 

§3.  Measurement  of  Current 

44.  The  Indications  of  Hot-wire  Instruments 67 

45.  Commercial  Hot-wire  Instruments 71 

46.  The  Hot-wire  Air  Thermometer 71 

47.  Bolometer,  Barretter 72 

48.  Thermoelement  or  Thermocouple 74 

49.  The  Thermogalvanometer ! 75 

50.  Comparison  of  the  Sensitiveness  of  Various  Measuring  Instruments .    .  76 

51.  Measurement  of  Very  Small  Currents 76 

CHAPTER  IV 

COUPLED  CIRCUITS 

§1.  Coupling  in  General 

52.  Magnetic,  Galvanic,  Electric  Coupling 79 

53.  Loose  and  Close  Coupling    .    .    .    •. 81 

54.  Methods  of  Coupling 82 

§2.  Loose  Coupling  of  Damped  Oscillating  Circuits 

55.  Coupling  of  Oscillator  to  Closed  Circuit 84 

56.  Extremely  Loose  Coupling  of  Two  Oscillators 85 

57.  Loose  Coupling  of  Two  Oscillators 87 

§3.  Close  Coupling  of  Tuned,  Damped  Oscillating  Circuits 

58.  Form  of  the  Oscillations 87 

59.  The  Frequency  of  Coupling  Waves 88 

60.  The  Decrements  of  Coupling  Waves 90 

61.  Amplitude  and  Phase  of  the  Oscillations 91 

§4.  Quenching  Action  in  Coupled  Circuits 

62.  Form  of  the  Oscillations 93 

63.  Various  Types  of  Quenched  Gaps 95 

64.  Requirements  for  Good  Quenching 95 

65.  Concerning  the  Nature  of  the  Quenching  Action 97 

§5.   The  Coupling  of  Undamped  Oscillating  Circuits 

66.  Coupling  with  a  Closed  Circuit 99 

67.  Loose  Coupling  with  an  Oscillator 100 

68.  Close  Coupling  with  an  Oscillator 101 

69.  Difference  between  Damped  and  Undamped  Oscillations 103 


CONTENTS  xiii 
CHAPTER  V 
RESONANCE  CURVES 

PAGE 
§1.  The  Resonance  Curve  of  the  Current  Effect 

70.  General  Remarks 104 

71.  Measurement  of  the  Frequency 106 

72.  Calibration  of  the  Measuring  Circuit 108 

73.  Determination  of  Capacities  and  Coefficients  of  Self  and    Mutual 
Induction  by  Resonance 112 

74.  Determination  of    the  Sum  of  the  Decrements  of  the  Primary  and 
Secondary  Circuits  (v.  Bjerknes) 113 

75.  Abnormal  Forms  of  the  Resonance  Curves 116 

76.  Determination  of  the   Decrements  of  the  Primary  and  Secondary 
Circuits 118 

77.  Measurement  of  Small  Changes  in  the  Decrement 120 

78.  Measurements  with  Resonance  Circuits  in  General 120 

79.  Commercial  "  Wavemeters" 125 

§2.  Resonance  Curve  of  the  Dynamometer  Effect  (L.  Mandelstam  and  N.  Papalexi) 

80.  General 132 

81.  Determination  of  the  Frequency  (Wave  length) 134 

82.  Decrement  Determination 135 

83.  The  Dynamometer 135 

§3.    Use  of  Resonance  in  the  Study  of  Condensers 

84.  Determination  of  the  Frequency  Factor 137 

85.  Energy  Absorbed  by  Dielectric  Hysteresis 138 

86.  The  Brush  Discharge  of  Condensers 138 

§4.   The  Use  of  Resonance  Curves  for  Investigating  Coupled  Circuits 

87.  Coupling  of  Tuned  Circuits 142 

88.  Close  Coupling  of  Tuned  Circuits 145 

89.  Coupling  Untuned  Circuits 147 

90.  Investigation  of  the  Quenching  Action  in  Spark  Gaps 148 

CHAPTER  VI 

THE  ANTENNA 

91.  General 150 

§1.  The  Various  Kinds  of  Antennae 

92.  Form  of  the  Aerials 150 

93.  Comparison  of  the  Different  Forms  of  Aerials 155 

§2.  Grounding 

94.  Ground  and  Counterpoise        . 157 

95.  Energy  Consumed  by  the  Earth  Currents 158 

96.  Ungrounded  Antennae  for  Airships 163 

§3.   The  Oscillations  of  Antennce 

97.  Frequency,  Capacity  and  Self-induction 164 

98.  Regarding  the  Effect  of  Coils 165 

99.  The  Damping  of  Antennae  and  Its  Causes 167 

100.  Determination  of  the  Decrement 168 


xiv  CONTENTS 

CHAPTER  Vll 

TRANSMITTERS  OF  DAMPED  OSCILLATIONS 

PAGE 

101.  The  Different  Types  of  Transmitters , 173 

§1.   The  Simple  (Marconi)  Transmitter 

102.  General 173 

103.  The  Damping 174 

§2.   The  Braun  Transmitter 

104.  Nature  of  the  Coupling 175 

105.  Coupled    Transmitter   for    Antenna?    Having    High   Damping.  Very 
Loose  Coupling 175 

106.  Coupled    Transmitter   for   Antennae   Having    High  Damping.    Close 
Coupling 176 

107.  Coupled  Transmitters  for  Slightly  Damped  Antennae 178 

108.  Commercial  Form  of  the  Braun  Transmitter 179 

§3.  Quenched  Spark  Gap  Transmitter  (Wien's  Transmitter) 

109.  Impulse  Excitation 182 

110.  The  Connections 184 

111.  Practical  Construction  of  Quenched  Spark  Gaps     .........  186 

112.  Commercial  Construction  of  the  Wien  Transmitter 192 

§4.  General  Consideration  of  Transmitters  of  Damped  Oscillations 

113.  Operation  by  Means  of  Interrupted  Direct  Current 194 

114.  Alternating-current  Operation     . 195 

115.  Direct-current  Operation      ......  i 198 

116.  Measurement  of  Energy  Supplied ;  Determination  of  the  Efficiency .    .  200 

117.  The  Key 202 

118.  Spark  Gaps  with  Rotating  Electrodes 203 

§5.  Comparison  of  the  Different  Types  of  Transmitters 

119.  Difference  between  the  Coupled  and  the  Simple  (Marconi)  Transmitter  208 

120.  Comparison  of  the  Braun  and  Wien  Transmitters 210 

CHAPTER  Vlll 
HIGH  FREQUENCY  MACHINES  FOR  UNDAMPED  OSCILLATIONS 

121.  The  Alexanderson-Fessenden  Machines 213 

122.  Goldschmidt's  High  Frequency  Generator .'." 216 

CHAPTER  IX 

UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD 

§1.  The  Various  Arrangements 

123.  The  Problem  and  the  Solution  by  V.  Poulsen 220 

124.  Commercial  Construction  of  the  Poulsen  Generators ........   222 

125.  Use  of  the  Poulsen  Arc  for  Measuring  Purposes  .    .    . 225 

126.  Circuit  Connections  of  the  Poulsen  Transmitter 227 

127.  Devices  for  Producing  Signals 228 

128.  The  Multitone  Transmitter  of  J.  C.  Lorenz 229 

§2.  Study  of  the  Action  of  the  Arc 

129.  Characteristic  of  the  Arc 231 

130.  Ty  pel  Oscillations:/!    <  70 233 


CONTENTS  XV 

PAGE 

131.  Type  11  Oscillations:  /IQ  >  70;  no  Re-ignition 234 

132.  Type  111  Oscillations:  IIQ  >  70;  Re-ignition  Present 236 

133.  Energy  of  the  Oscillations 237 

134.  Frequency  of  the  Oscillations  215 238 

135.  Practical  Conclusions  for  Type  11  Oscillations 239 

136.  Regularity  of  Type  11  Oscillations 241 

137.  The  Terms  "Spark"  and  "Arc"217 245 

CHAPTER  X 

PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE 

§1.  Over  Plane  or  Spherical  Homogeneous  Ground 

138.  Ground  Having  Plane  Surface  and  High  Conductivity 246 

139.  Over  Flat  Ground  of  Not  Very  High  Conductivity 248 

140.  Effect  of  the  Spherical  Shape  of  the  Earth 255 

§2.   Wave  Propagation  over  Uneven  or  Non-homogeneous  Ground 

141.  Uneven  Surfaces 258 

142.  Rain  and  Ground  Water 260 

143.  Distribution  over  Land  and  Water 262 

§3.  Effect  of  Atmospheric  and  Other  Influences  upon  the  Waves 

144.  Effect  of  the  Condition  of  the  Atmosphere 263 

145.  lonization  of  the  Atmosphere 264 

146.  Actual  Measurements  of  the  Wave  Propagation 269 

147.  Effect  of  Grounding  the  Transmitter  upon  the  Wave  Propagation  .    .  270 

148.  The  Safety  Factor 271 

CHAPTER  XI 

DETECTORS247 

§1.   Thermal  Detectors 

149.  Bolometer  and  Thermogalvanometer .    . 272 

.   150.  Thermocouples,  Thermal  Detectors .  273 

151.  Relative  Importance  of  the  Thermal  Detectors 274 

§2.  Magnetic  Detectors251 

152.  The  Fundamental  Physical  Principles 274 

153.  Marconi's  Magnetic  Detector 274 

154.  Other  Forms  of  Magnetic  Detectors 275 

§3.  Imperfect  Contacts 

155.  Metallic  Granular  Coherer255 276 

156.  Mercury  Coherers 278 

157.  Carbon  or  Graphite  Coherers.      (Microphone  Contact) 279 

§4.  Electrolytic  and  Other  Detectors 

158.  Anticoherers 279 

159.  The   Electrolytic    Detectors   of   FERRIE,  FESSENDEN,    NERNST,    and 
SCHLOMILCH 280 

160.  Crystal  Detectors 282 

161.  Incandescent  Lamp  Detectors.     Gas  Detectors 283 

§5.  General  Consideration  of  Detectors 

162.  The  Nature  of  the  Action  in  Various  Detectors 285 

163.  What  do  the  Different  Types  of  Detectors  React  upon? 287 

164.  Testing  the  Sensitiveness  of  Detectors 289 


xvi  CONTENTS 

PAGE 
§6.  Receiving  Apparatus 

165.  Telephone  Reception 290 

166.  Amplification  of  the  Sound  in  Telephone  Reception 291 

167.  Automatic  Recording  of  Messages 294 

168.  Recording  Apparatus  for  the  Metallic  Granular  Coherer 298 

169.  Call  Signals 299 

170.  Comparison  of  the  Different  Kinds  of  Detectors 300 

CHAPTER  Xll 
RECEIVERS 

171.  The  Aerials  of  the  Receiving  Stations .   303 

172.  General  Consideration  of  the  Receiving  System 304 

§1.   The  Original  Marconi  Receiver 

173.  The  First  Arrangement 307 

174.  The  Marconi  Transformer 308 

§2.  Receivers  for  Tuned  Telegraphy  with  Damped  Oscillations 

175.  Receivers  for  Highly  Damped  Receiving  Antennae 310 

176.  Receivers  for  Weakly  Damped  Antennae 313 

177.  Tuning  the  Receiver  for  a  Double  Wave  Transmitter 314 

178.  Adjustment  of  the  Energy  Delivered  to  the  Receiver 314 

179.  Receivers  for  Two  Different  Detectors 315 

180.  The  Sharpness  of  Tuning 316 

181.  R.  A.  Fessenden's  Method  for  Maintaining  Secrecy  of  Telegrams.    .    .   323 

182.  Multiple  Telegraphy 324 

183.  Methods  for  Overcoming  Atmospheric  Disturbances 326 

184.  Achievements  of  Tuned  Telegraphy 328 

185.  Methods  for  Preserving  Secrecy  of  Messages 330 

§3.  Receivers  for  Undamped  Oscillations 

186.  General 332 

187.  Methods  Employing  the  Ordinary  Detector 333 

188.  The  Ticker '334 

189.  Construction  of  Interrupter  for  Ticker  Method 335 

190.  Special  Arrangements  for  Undamped  Oscillations 335 

191.  Practical  Achievements 336 

CHAPTER  Xlll 
DIRECTIVE  TELEGRAPHY 

192.  Characteristic  of  the  Distance  Effect 338 

§1.  The  First  Attempts 

193.  Use  of  Reflectors 340 

194.  Attempts  at  Screening 340 

§2.  Methods  Employing  Several  Antennce 

195.  The  Field  of  Several  Antennae — General  Consideration 341 

196.  The  Field  of  Several  Antennae— Special  Cases 342 

197.  Double  Antennae,  One-half  Wave  Length  Apart 345 

198.  The  Methods  of  E.  Bellini  and  A.  Tosi 347 

199.  The  Methods  of  F.  Braun   .  .  352 


CONTENTS  xvii 

PAGE 

200.  Production  of  Any  Desired  Phase  Difference  with  Undamped  Oscil- 
lations  352 

201.  Production  of  Any  Desired  Phase  Difference  with  Damped  Oscillations  353 
§3.  Aerials  Having  Horizontal  or  Inclined  Portions 

202.  Marconi's  Bent  Antenna 356 

203.  The  Action  of  the  Bent  Marconi  Antenna  when  Transmitting  ....  357 

204.  The  Bent  Marconi  Antenna  Used  for  Receiving 361 

205.  Inclined  Antennae 363 

206.  Horizontal  Antennas.     Ground  Antennae 364 

207.  The  Advantages  of  Directive  Signalling 365 

CHAPTER  XIV 

WIRELESS  TELEPHONY 

§1.  The  Transmitter 

208.  Source  of  Energy 371 

209.  Connections 371 

210.  Microphones 373 

§2.  The  Receiver 

211.  Connections 374 

212.  The  Action  in  the  Detector  Circuit 376 

The  Development  of  Wireless  Telegraphy  During  the  Years  1909-1912 

TABLES 

Table         1.  The  Natural  Frequency  of  Condenser  Circuits 384 

"  11.  The  Natural  Wave  Length  of  Condenser  Circuits 386 

"         111.  Frequency  and  Wave  Length 388 

"          IV.  Oscillation  Curves  for  Various  Decrements 389 

V.  The  Spark  (Arc)  Constants 392 

"          VI.  Equations  for  Calculations  of  the  Coefficient  of  Self-induction    .    .  393 

"        VII.  Effective  Resistance  of  Copper  Wires 396 

"      Vlll.  Maximum  Diameter  of  Resistance  Wires 398 

"         IX.  Gap  Lengths  and  Corresponding  Minimum  Discharge  Voltages .    .    .  399 

X.  Determination  of  Percentage  Coupling 401 

"         XL  Resonance  Curve  of  the  Current  Effect 403 

"        Xll.  Resonance  Sharpness 405 

"      Xlll.  The  Radiation  Resistance  of  Antennae 405 

BIBLIOGRAPHY  AND  NOTES  ON  THEORY 
INDEX  .  408 


SYMBOLS  AND  ABBREVIATIONS 

The  following  explanations  of  symbols  and  abbreviations  used  in  the  text  apply 
throughout  unless  distinctly  stated  otherwise : 
E  =  Electric  field  strength 
M  =  Magnetic  field  strength 
8  =  Electromotive  force  =  e.m.f. 
IJL  —  Permeability 
e  =  Dielectric  constant 
€o  =  Dielectric  constant  of  air 

k  =  — ,  usually  referred  to  as  the  dielectric  constant 

mf.  =  Microfarad 
c.g.s.  =  Units    of    the    absolute    electromagnetic     (centimeter-gram-second) 

system 

S  =  Radiation 
W  =  Energy 

We  =  Energy  of  the  electrical  field 
Wm  =  Energy  of  the  magnetic  field 
V  =  Voltage 
Vz  =  Ignition  voltage 

/  =  Current  (frequently  i  is  used  in  the  illustrations) 
r  =  Resistance 

Ls  =  Coefficient  of  self-induction     !•   for  stationary  field 
Cs  =  Capacity 
R  =  Resistance 


L  =  Coeff.  of  self-induction 


for  oscillations 


C  =  Capacity 
i^  or  Ls2]L  =  Coeff.  of  mutual  induction  with  quasi  stationary  current 

Z/i2  or  L2l  =  Coeff.  of  mutual  induction  with  non-quasi  stationary  current 

Ro  =  Gap  resistance 

RZ  =  Radiation  resistance 

K  =  Coeff.  of  coupling 

K'  =  Degree  or  percentage  of  coupling 

T  =  Period 

N  =  Frequency  =  number  of  complete  periods  per  second 

co  =  2-n-T  =  -^  =  number  of  periods  in  2ir  seconds  =  circuit  frequency 

X  =  Wave  length 
VL  =  Velocity  of  propagation 

f  =  Discharge  frequency  =  number  of  discharges  per  second 

d  =  (Logarithmic)  decrement 
dj  =  Joulean  decrement 
dh  =  Hysteresis  decrement 
ds  =  Radiation  decrement 
dg  =  Gap  decrement 

a  =  Lineal  decrement 

xix 


XX  SYMBOLS  AND  ABBREVIATIONS 

a  =  Form  factor  of  an  antenna 
p  =  Sharpness  of  resonance 
a,  b  =  Constants  of  the  spark  or  arc 

e  =  Base  of  the  natural  (Naperian)  logarithms 
a   =  Proportional  to;  varies  as 
<^  =  Much  less  than 
^>  =  Much  greater  than 

EMS  =  Zenneck's    "Elektromagnetische    Schwingungen    u.    drahtlose    Tele- 
graphic."    Stuttgart,  1905. 
ETZ  =  Elektrotechnische  Zeitschrift 
Jahrb.  =  Jahrbuch  fur  drahtlose  Telegraphic.     Leipzig.     Joh.  Amer.  Barth. 

El.  =  The  Electrician.     London. 
C.R.  =  Comptes  rendus  de  1'Academie  des  Sciences.     Paris. 


WIRELESS  TELEGRAPHY 

CHAPTER  I1 
THE  NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS 

1.  Oscillations  Produced  by  Charging  the  Condenser. — The  simplest 
form  of  a  condenser  circuit  is  that  shown  in  Fig.  1 :  a  condenser,  C,  and 
a  conductor,  AFB,  joining  the  metallic  coatings  of  the  condenser. 

a.  Let  this  circuit  be  broken  at  some  point,  F,  and  each  side  connected 
to  one  pole  of  an  electric  influence  machine,  an  induction  coil  or  an 
alternating-current  transformer  (Fig.  2).  If  then  the  influence  machine 
or  induction  coil  is  put  into  operation,  the  condenser  becomes  charged, 
one  of  its  coatings,  say  A,  receiving  a  certain  quantity  of  positive  elec- 


To  Induction  Coil 

FIG.  2. 

tricity,  the  other,  B,  an  equal  amount  of  negative  electricity.  The 
resultant  electrical  field  and  difference  of  potential  are  obtained  not  only 
between  the  coatings  A  and  B}  but  also  between  the  poles  FI  and  F2 
of  the  gap  in  the  circuit.  If  the  condenser  charge  and  thereby  the  tension 
between  FI  and  F2  are  gradually  increased,  a  "spark"  finally  passes  be- 
tween Fi  and  F2  and  the  space  FiF2,  the  "spark  gap,"  becomes  conductive. 
6.  The  difference  in  potential  between  the  coatings  A  and  B  produces 
an  electric  current  in  the  direction  of  the  arrow  in  Fig.  2,  from  the  positive 
to  the  negatively  charged  coating.  This  holds  good  only  at  the  start, 
however.  For  the  current,  assuming  that  the  resistance  of  the  conductors 

1 


WIRELESS  TELEGRAPHY 


is  not  extremely  high,  is  an  oscillating  or  alternating  current 
of  the  kind  represented  by  the  curve  in  Fig.  3,  a  photographic  reproduction 
made  by  the  aid  of  BRAUN'S  Kathode  Ray  Tube,2  which  is  specially 
adapted  for  such  purposes.  The  absciss®  of  the  curve  are  proportional 
to  the  time,  the  ordinates  to  the  current  values  at  any  instant. 

This  alternating  current  is  in  one  respect  distinctly  different  from  the 
alternating  currents  in  ordinary  commercial  use  as  produced  by  A.C. 
generators,  viz.,  it  has  a  constantly  decreasing  amplitude.  An  alternating 
current  of  this  kind  is  said  to  be  "damped"  to  distinguish  it  from  an 
"undamped"  alternating  current  of  constant  amplitude. 

c.  As  every  current  produces  a  magnetic  field  whose  strength,  at 
least  in  the  vicinity  of  the  current-carrying  conductor,  is  proportional  to 
the  current,  it  may  be  concluded  that  the  magnetic  field  varies  similarly 
to  the  current;  it  is  a  "damped  alternating  magnetic  field." 


''"... 


»M«. 


Time 

FIG.  3. 

During  the  period  in  which  the  current  has  the  direction  shown  in 
Fig.  2,  it  must  bring  a  positive  charge  from  the  coating  A  to  B,  and 
when  its  direction  is  reversed,  its  action  upon  the  condenser  coatings  is 
also  reversed.  Hence  the  condenser  charge  also  %  oscillates  and  the 
electric  field  between  its  coatings  is  also  a  damped  alternating  field. 

d.  The   entire   phenomenon,   i.e.,   the   alternating   current   with   its 
accompanying   alternating   electric    and    magnetic    fields    is   called    an 
"electromagnetic  oscillation." 

Oscillations,  which,  as  in  this  case,  may  be  produced  in  a  condenser 
circuit  without  the  influence  of  other  oscillations,  are  said  to  be  the 
"natural"  or  "free  oscillations"  of  that  circuit. 

e.  With  the  arrangement  of  Fig.  2,  the  natural  oscillations  are  caused 
by  the  spark.     In  general,  however,  the  presence  of  a  spark  is  not  essential 
for  the  production  of  natural  oscillations,  which  may  also  be  obtained  in 
a  condenser  circuit  having  no  spark  gap  [Art.  109]. 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS  3 

1.  FREQUENCY 

2.  Experimental  Determination  of  the  Frequency. — a.  Even  with 
condenser  circuits,  whose  natural  oscillations  are  too  rapid  to  allow  of 
photographic  reproduction  by  the  aid  of  a  Braun  tube  (see  Fig.  3)  or  an 
oscillograph,  the  "frequency"  of  the  oscillation,  i.e.,  the  number  of 
complete  cycles  per  second,  can  be  directly  determined  by  means  of  a 
rotating  mirror — FEDDERSEN'S  method — if  the  condenser  circuit  contains 
a  spark  gap.  The  gap,  placed  in  a  horizontal  position  and  viewed  in  a 
mirror  which  rotates  about  a  horizontal  axis — e.g.,  fixed  on  the  shaft  of 
a  small  electric  motor  (Fig.  4) — appears  during  a  discharge  in  the  form 
shown  in  Fig.  5.  At  those  moments  during  which  the  current  passing 
over  the  gap  is  a  maximum,  the  most  light  is  produced  in  its  path,  which 
is  very  dark  when  the  current  is  at  its  minimum;  so  that  the  illumination 


FIG.  4. 

of  the  path  of  the  discharge  varies  periodically  with  the  current.  Hence, 
in  the  rotating  mirror,  in  which  the  successive  images  of  the  spark  appear 
at  different  points,  a  row  of  alternately  light  and  dark  stripes  is  obtained. 

The  distance  between  two  adjacent  light  stripes  corresponds  to  the 
time  of  a  half  period  of  the  oscillation.  If  the  image  in  the  rotating  mirror 
is  photographed  and  if,  from  the  number  of  revolutions  of  the  mirror  and 
the  dimensions  of  the  apparatus,  the  speed  with  which  the  image  of  the 
spark  moves  over  the  photographic  plate  is  determined,  then  the  time  of 
one  cycle  and  hence  the  frequency  of  the  oscillations  are  easily  obtained 
from  the  distance  between  two  or  more  light  stripes. 

This  method  is  not  only  of  great  practical  value,  but  is  of  special 
interest  as  having  been  used  by  W.  FEDDEESENS  in  the  first  experimental 


WIRELESS  TELEGRAPHY 


m 

m 


FIG.  5. 


demonstration  and  study  of  the  natural 
oscillations  of  condenser  circuits,  which 
constitute  the  foundation  of  the  science 
of  modern  radio-telegraphy. 

b.  Gehrke's  incandescent  oscillo- 
graph tube  offers  another  method  for 
the  direct  determination  of  the  fre- 
quency of  condenser  circuits.4 

It  consists  of  a  glass  tube  of  the 
form   shown  in  Fig.  6a,  with  wire  or 
sheet  metal  electrodes  (Fig.  66)  and 
filled  with  pure  nitrogen  under  slight 
pressure.     If  current  is  sent  through 
this  tube,  the  length  of  the  incandes- 
cent portion  of  the  negative  electrode 
is  approximately  proportional  to  the 
strength  of  the  current.     If  the  tube  is 
connected  through  a  sufficiently  high 
series  resistance  (tube  of  water,  R,  in 
Fig.  7)  to  the  condenser  coatings,  then 
the  current  passing  through  it,   and 
hence  also  the  length  of  the  incandes- 
cence, are  proportional  at  any  instant 
to  the  voltage  between  the  condenser 
coatings.     By  photographing  the  image  of  the  tube  in 
a  mirror  whose  axis  is  parallel  to  the  axis  of  the  tube 
(Fig.  8)*,  a  picture  of  the 
form  shown  in  Fig.  9  (H. 
DiESSELHORST)4    is     ob- 
tained.    The  distance  be- 
tween the  light  stripes  is 
a  measure  of  the  duration 
of  a  cycle  (see  a). 

As  this  tube  absorbs 
considerable  energy  and  as 
the  length  of  the  negative 
incandescence  is  not  al- 
ways exactly  proportional 
to  the  amount  of  current 
passing  through  it,  it  is 
adapted  for  demonstration  purposes  rather  than  for  accurate  measurements. 

*  Fig.  8  shows  oscillograph  made  by  the  firm  H.  Boas  :  the  tube  is  in  a  box  at  the 
upper  right  and  below  this  is  the  holder  for  trie  photographic  plate  upon  which  the 
concave  mirror,  mounted  on  the  shaft  of  the  motor,  reflects  the  image  of  the  tube. 


FIG.  6a.    FIG. 


/i 


(mm 


FIG.  7. 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS 


c.  More  convenient  but  indirect  methods  for  determining  the  frequency 
will  be  discussed  later  [Art.  71,  81]. 


FIG. 

3.  Calculation  of  Frequency  (THOMSON'S  Equation) . — a.  The  follow- 
ing formula  for  the  natural  frequency,  N,  of  condenser  circuits  has  been 
deduced  by  LORD  KELVIN  (SiR 
WILLIAM  THOMSON5'1) : 

•  ^  777^     [Table  I]* 
1 


CO    = 


VLC 


t 


in  which  L  is  the  coefficient  of  self- 
induction  of  the  circuit  and  C  its 
capacity,  while  o>  is  the  number  of 
oscillations  in  2w  seconds.  Simi- 
larly  the  period,  T,  of  the  oscillation  is  given  by 


FIG.  9. 


T=  ~  = 


*  This  relation  holds  only  if  the  damping  is  not  extremely  great  (i.e.,  d  <  2-n-)  and, 
therefore,  applies  to  all  practical  cases.     The  exact  formula  is: 


where  d  =  the  decrement  [Art.  8]. 

t  The  wave  length  [Art.  19]  is  given  b 

'  =  6*-  VLCGS  . 


.  1010  cm. 


\/L 


CGS 


MP 


meters 


—  59.61-v/L^rr  ,<?  •  CM™  —  infk 


C.G.8.  '  °cm.  meterS 


(Table  II) 


6  WIRELESS  TELEGRAPHY 

It  follows  that  for  a  condenser  circuit  of  a  given  frequency,  the  product 
of  its  capacity  and  self-induction  is  a  fixed  quantity. 

b.  If  the  frequency  is  to  be  obtained  in  cycles  per  second,  L  and  C 
must  be  expressed  in  units  of  the  same  absolute  system.  In  the  following, 
unless  otherwise  stated,  the  customary  absolute  magnetic  system,  known 
as  the  C.G.S.  system  (centimeter,  gram,  second-system)  is  used. 

The  unit  of  capacity  customary  in  practice,  the  microfarad  (MF),  is 
Koll5J°f  the  C.G.S.  unit.*  A  Leyden  jar  of  average  size  usually  has  a 
capacity  of  several  thousandths  of  a  MF. 

The  henry,  which  is  the  customary  unit  for  the  coefficient  of  self- 
induction  is  equal  to  109  C.G.S.  units.  In  wireless  telegraphy,  however, 
it  is  more  convenient  to  express  the  coefficient  of  self-induction  in  C.G.S. 
units,  instead  of  in  henrys,  as  the  circuits  used  for  radio-telegraphy 
usually  have  coefficients  of  self-induction  of  much  less  than  1  henry. 

4.  Condensers  in  Series  and  in  Parallel. — The  term  "resultant 
capacity"  of  a  number  of  condensers  in  what  follows  will  be  understood 

ToInd.Coil 


ToInd.Coil 

FIG.  10.  FIG.  11. 

as  that  value  of  the  capacity,  which,  when  substituted  for  C  in  Thomson's 
equation,  gives  the  correct  value  of  the  frequency. 

a.  Where   large    capacities   are   required,   several    condensers    must 
usually  be  joined  in  " parallel"  (Fig.  10). 

If  Ci  and  C2  represent  the  respective  capacities  of  the  two  condensers 
in  Fig.  10,  then  the  resultant  capacity  of  the  condensers  in  parallel  =  the 
sum  of  their  individual  capacities,  i.e., 

C  -  d  +  Ci 

If  M  number  of  condensers,  each  having  a  capacity  C\,  are  connected  in 
parallel  the  resultant  capacity  C  =  M  d. 

b.  Sometimes  it  may  be  necessary  to  connect  a  number  of  condensers 

*  Frequent  use  is  also  made  in  practice  of  the  absolute  electric  system  unit  of 
capacity,  the  cm.  Where  formulas  involving  the  cm.  are  given  in  this  book,  this  is 
done,  however,  only  in  consideration  of  current  practice. 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS 


in  " series"  (Fig.  11).  In  this  case  the  resultant  capacity  C  is  obtained 
from  the  relation 

1  _    JL    ,JL 

C  ~~  C\  +  C2 
so  that  if  Ci  =  C2,  we  have 

c-lc 

~  2Cl 

If  one  of  the  condensers  in  series  has  a  capacity  Ci  which  is  very  much 
greater  than  that,  C2,  of  the  other,  the  resultant  capacity,  C,  is  approxi- 
mately equal  to  C2,  i.e.,  it,  as  well  as  the  frequency,  is  dependent  mainly 
upon  the  smaller  capacity. 


To  Ind.  Coil 


FIG.  12. 


To  Ind.  Coil 
FlG.    13. 


c.  Figs.  12  and  13  show  combinations  of  series  and  parallel  connec- 
tions frequently  occurring  in  practice.  The  resultant  capacity  in  each 
case,  as  is  easily  obtained  from  the  preceding,  is, 

1 


and 


Fig  13:         ' 


+  7i 


1 


"i    /~i  ' i   /•> 


f-  C2  +  Cz        Ci  +  Cs  +  CG 

If  all  the  condensers  are  of  equal  capacity  Ci,  then 

r^  r< 

so  that  the  resultant  capacity  of  the  given  combinations  of  four  and  nine 
condensers  is  the  same  as  that  of  any  one  of  the  condensers  placed  in  the 
circuit  as  shown  in  Fig.  1. 

d.  Hence,  so  far  as  the  resultant  capacity  is  concerned,  the  combina- 


8  WIRELESS  TELEGRAPHY 

tions  of  Figs.  12,  13  and  2,  assuming  all  the  individual  condensers  to  be 
of  equal  size,  are  exactly  alike.  The  difference,  this  being  one  of  the 
advantages  of  the  combined  series  and  parallel  connections  as  compared 
to  the  single  condenser,  lies  in  the  distribution  of  the  charge  among  the 
individual  condensers.  In  Fig.  2  the  potential  across  the  condenser  is 
the  same  as  that  between  the  electrodes  of  the  spark  gap,  while  the 
potential  across  each  condenser  in  Fig.  12  is  only  one-half  the  total  gap 
potential  and  in  Fig.  13  only  one-third  of  the  gap  potential. 

5-  The  Practical  Importance  of  Thomson's  Equation. — THOMSON'S 
equation  offers  a  very  simple  means  for  rough  calculations  in  determining 
an  approximate  value  of  the  frequency  or,  on  the  other  hand,  the  value 
of  the  capacity  required  for  a  given  frequency.  Usually,  however,  it 
is  not  possible  to  determine  these  values  with  the  accuracy  required  in 
practice.  Not  that  the  Thomson  formula  is  inaccurate,  but  in  con- 
denser circuits  having  no  spark  gap,  for  which  alone  the  Thomson  rela- 
tion holds  good,  the  value  of  the  capacity  and  coefficient  of  self-induc- 
tion are  mostly  not  known  exactly;  in  condenser  circuits  with  a  spark 
gap,  the  spark  affects  the  frequency. 

a.  The  values  of  C  and  L  substituted  in  Thomson's  equation  must,  of 
course,  be  those  which  correspond  to  that  frequency  which  is  to  be 
determined. 

For  air  condensers  the  capacity  C,  under  the  conditions  prevalent 
in  wireless  telegraph  work,  is  practically  the  same  as  the  capacity  C8 
of  the  same  condenser  holding  a  static  charge,  and  can  therefore  be  easily 
measured  with  sufficient  accuracy. 

For  condensers,  however,  having  a  solid  or  liquid  dielectric,  the 
capacity  may  vary  widely  with  the  frequency.  The  ratio  between 
capacity  C  of  a  condenser  in  an  oscillating  circuit  to  its  capacity  C8 
for  a  static  charge  is  termed  the  " frequency  factor."  When  mica  or 
micanite  is  used  as  the  dielectric  this  factor  may  be  as  low  as  0.7-0.8, 
and  for  certain  kinds  of  glass  it  may  differ  considerably  from  1.0,  while  for 
other  varieties,  as  for  example  certain  flint  glasses,  and  particularly  for 
certain  oils,  such  as  petroleum  or  well-dried  paraffin  oil,  the  frequency 
factor  is  practically  unity.6 

b.  That  care  must  be  taken  in  choosing  the  proper  value  of  L,  the 
coefficient  of  self-induction,  for  use  in  Thomson's  equation  follows  from 
the  fact  that  the  value  of  L  may  be  quite  different  for  the  same  coil  with 
an  alternating  than  with  a  direct  current  [Art.  35]. 

A  further  complication  arises  from  the  fact  that  L  is  the  coefficient  of 
self-induction  of  the  entire  circuit.  For  example  in  the  case  of  Fig.  10 
this  comprises  not  only  the  main  conductor  AFB,  but  also  the  con- 
denser coatings  and  their  leads  (ACi,  BCi,  AC2,  BCZ).  However,  if  the 
circuit  contains  a  coil  of  several  turns  this  need  not  be  considered,  as  the 
rest  of  the  circuit  adds  very  little  to  the  relatively  large  coefficient  of 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS  9 

self  -induction  of  the  coil  and  may  be  neglected  without  materially  im- 
pairing the  accuracy.  But  in  some  cases  it  is  desirable  to  keep  the  self- 
induction  of  the  circuit  AFB  (Fig.  10)  as  low  as  possible  and  it  may 
happen,  especially  when  using  a  larger  number  of  condensers  with 
their  connections,  that  the  resultant  coefficient  of  self-induction  is  much 
greater  than  the  value  calculated  from  the  general  dimensions  of  the 
circuit  AFB. 

c.  The  frequency  of  condenser  circuits  containing  a  spark  gap  may 
vary  as  much  as  10  per  cent,  from  that  indicated  by  Thomson's  equation 
(M.  WIEN,  H.  RiEGGER7).  However,  this  variation  is  great  only  if  the 
electrodes  of  the  spark  gap  are  made  of  copper  or  silver  and  if  the  gap 
itself  is  at  the  same  time  very  short  (say  ^  2  mm.)*  the  variation  be- 
comes greater  in  proportion  to  the  shortness  of  the  gap  and  the  small- 
ness  of  the  condenser,  other  things  being  equal. 

If  tin,  zinc,  cadmium  and  especially  magnesium  are  used  for  the 
electrodes  and  if  the  gap  length  is  greater  than  4  or  5  mm.,  the  frequency 
can  be  determined  from  THOMSON'S  equation  within  a  fraction  of  1  per 
cent,  for  condenser  circuits  including  a  spark  gap,  assuming  of  course 
that  the  values  of  L  and  C  are  accurately  known.8 

2.  THE  DAMPING 

6.  The  Transfer  of  Energy.  —  a.  As  long  as  the  current,  7,  has  the 
direction  of  the  arrow  in  Fig.  2,  positive  electricity  is  flowing  away  from 
the  condenser  coating  A,  so  that  the  positive  charge,  +  e,  of  this  coating 
is  decreasing.  When  the  current  is  reversed  this  charge  is  increasing. 

The  same  applies  to  the  potential  difference,  V,  between  the  con- 
denser coatings,  as  this  and  the  charge  hold  the  well-known  relation: 

e  =  CV 

If  curves  be  plotted  showing  the  variation  of  V  and  7  respectively 
as  ordinates  with  the  time  as  abscissae,  the  results  will  be  as  in  Fig. 
14.  Voltage  and  current  have  a  phase  displacement  of  practically  90°. 

b.  The  energy  We,  in  the  electric  field  of  a  condenser  of  capacity  C, 
charged  to  a  potential  V,  is  known  to  be 


Similarly  the  energy  Wm  in  the  magnetic  field  of  a  circuit  whose  coefficient 

of  self-induction  is  L  [9],  is  known  to  be 

«^ 

Wm  =  \  LI2 

*  Translators'    Note:   Just   these   conditions   prevail   in  the  modern  quenched 
spark  gap.  —  A.  E.  S. 


10 


WIRELESS  TELEGRAPHY 


where  /  is  the  current  flowing  in  the  circuit.  And  the  total  energy  of  the 
field  of  the  condenser  circuit  at  any  moment  is  equal  to  the  sum  of  the 
energies  of  the  electric  and  the  magnetic  fields,  i.e., 

W    =    We  +    W  m 

c.  Fig.  15  shows  We  (broken  line),  W m  (thin  full  line)  and  W,  the  sum 
of  the  other  two  (heavy  full  line).  The  current  curve,  /,  from  Fig.  14 
has  also  been  drawn  in  again  for  direct  comparison. 


I      I      i      I      I     I      !      '      I      !      I     I     i     I      I     I     I 


Time 


Timer 


At  the  start  when  the  current  is  zero,  we  have 

W  =  We 

i.e.,  the  total  energy  of  the  circuit  consists  of  the  electric  energy  of  the 
charged  condenser. 

One-quarter  of  a  period  later  the  voltage  is  zero  (Fig.  14)  and  the 
current  is  just  at  its  maximum.     We  then  have 

W  =  Wm 

or  the  total  energy  of  the  condenser  circuit  is  equal  to  that  of  its  magnetic 
field. 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS 


11 


After  another  quarter  period  the  current  is  zero  again  and 
W  =  We,  and  so  on. 

In  short,  the  oscillations  are  really  interchanges  of  the  energy  between 
the  electric  field  of  the  condenser  and  the  electromagnetic  field  produced 
by  the  current. 

7.  The  Various  Causes  of  Damping. — a.  If  no  energy  were  consumed 
by  this  transfer,  the  total  energy  W  and  also  the  current  and  voltage 
amplitudes,  in  view  of  the  relations  explained  in  Art.  66,  would  remain 
constant.  Any  consumption  of  energy,  however,  means  a  reduction  in 


FIG.  15 


the  total  energy,  i.e.,  a  decreasing  amplitude,  resulting  in  a  " damping" 
of  the  oscillations.  The  question  of  the  various  causes  of  damping  is 
therefore  identical  with  the  question  of  the  various  energy  losses. 

b.  The  energy  lost  in  the  oscillations  of  condenser  circuits  can  be 
divided  as  follows :  that  lost  in 

1.  Heat  developed  in  the  metallic  circuit. 

2.  The  spark  gap. 

3.  The  insulation  of  the  condensers.* 

4.  " Brush"  leakage  of  the  condensers. 

5.  Eddy  currents  induced  by  the  alternating  magnetic  field  of  the 
current,  f 

8.  Condenser  Circuit  without  Spark  Gap  Damping  Due  to  Heat 
Loss. — a.  The  heat  developed  by  a  direct  current  /  in  a  conductor  of 
resistance  r  during  the  time  t  is 

rlH 

*  And  possibly  also  in  the  insulation  of  the  coils  [Art.  37c]. 
f  The  energy  lost  by  radiation  is  extremely  small  [Art.  25e]. 


12  WIRELESS  TELEGRAPHY 

while  for  an  alternating  current  during  the  time  of  one  cycle  T  the  heat 
developed  is 


where  R  is  the  "effective"  resistance  and  I\ff  is  the  mean  value  of  72, 
Ieff  being  the  "effective"  current.  For  undamped  oscillations,  the  wave 
form  being  sinusoidal, 

/Vr -!/•.. 

(where  Imax  is  the  maximum  amplitude  of  the  current  for  that  cycle) 
which  relation,  however,  is  also  practically  true  of  the  damped  oscillations 
to  be  considered  in  wireless  telegraphy.  Under  these  conditions  there- 
fore the  heat  developed  per  cycle  is 

1 
2 

From  Art.  66  and  6c  it  follows  that  the  total  energy  transferred  in  one 
cycle  (two  alternations)  is 

-2X2  LI2max  =  LI2max 

Hence  the  energy  lost  in  heat  is  proportional  to  the  total  energy  of  the 
oscillations  of  a  condenser  circuit. 

6.  If  the  energy  lost  in  heat  is  the  only  loss,  then  it  can  be  demonstrated 
that  the  curve  showing  the  decrease  in  the  amplitude  with  time — the 
amplitude  curve" — is  an  exponential  curve.  Its  characteristic  property 
is  the  fact  that  the  ratio  of  the  amplitude,  A  i,  at  the  beginning  of  a  cycle 
to  that,  A  2,  at  the  end  of  the  same  cycle  remains  constant  during  the  entire 
oscillation,  i.e., 

-j-  =    const.  (1) 

The  greater  this  ratio  is,  the  greater  is  the  percentage  decrease  in 
amplitude  per  cycle.  Hence  the  value  of  this  ratio  is  a  measure  of 
the  damping.  Instead  of  the  ratio  itself,  however,  it  is  customary  to  use 
the  natural  logarithm  of  its  value: 

d  =  log  nat.  j-1  (2) 

d  is  called  the  "logarithmic  decrement"  or  simply  "decrement"  and 
where  the  heat  loss  is  the  only  cause  of  damping,  as  in  the  preceding,  it  is 
distinguished  as  the  "Joulean  decrement,"  d,-. 

c.  The  value  of  the  amplitude  A  at  any  time,  t,  is  given  by 


A  =  A*        =  A*'  (3) 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS 


13 


in  which  N  is  the  frequency,  e  is  the  base  of  the  natural  logarithms  and 
AQ  is  the  "initial  amplitude"  when  t  =  0.* 

Fig.  16  shows  the  decrease  in  amplitude  per  cycle  for  different  decre- 
ments, while  in  Table  IV  the  oscillation  curves  have  been  drawn  out  for 
various  decrements. 

d.  It  follows  from  a  that  the  Joulean  decrement  can  be  determined 
from  the  ratio  of  the  energy  lost  in  one  cycle  to  that  transferred  in  the 
same  cycle.  Hence,  substituting  70  for  Imax,  we  have 


a> 


LI 


__    B  _R_ 

~  2L     1        2NL 


or  replacing  T  by 


123456789       10 
Number  of  Cycles  or  Periods 

FIG.  16. 


(Art.  3a)  we  have 


or  from  the  foot-note  in  Art.  3a 


RC 
X 


9.  Condenser  Circuit  with  Spark  Gap.     Damping  due  to  Spark. — 

a.  The  curves  AI  and  A2  of  Fig.  17  are  the  amplitude  curves  of  condenser 
circuits  containing  a  spark  gap  (J.  ZENNECKIQ)  obtained  with  the  Braun 
Tube,  AI  being  for  a  circuit  of  very  low,  A2  for  one  with  higher  ohmic 
resistance.  Comparison  with  Fig.  16  shows  a  marked  difference  from 
the  cases  in  which  the  damping  is  due  to  heat  loss  only.  The  amplitude 


*  In  Fig.  14,  V0  in  the  upper,  70  in  the  lower  curve. 

,     ,  Af.n     ,      Rohms  .  CMF  Cftor.    Rohm,  .  CMF  Rohms 

t  dj  =  6007T2 —        -   =  5920  — - —        —  or  =  ^7:7^  ' 

^meters  A  meters  lOU  .  . 


approximately. 


14 


WIRELESS  TELEGRAPHY 


curve  is  now  no  longer  an  exponential  curve  but  approaches  a  straight 
line  more  and  more  as  the  energy  absorbed  by  the  spark  exceeds  the 
energy  lost  as  heat.10  This  condition  is  obtained  when  the  spark-gap 
electrodes  are  of  copper,  brass,  aluminium  or  silver, n  while  with  magnesium 
electrodes  the  amplitude  curve  tends  toward  the  exponential  form 

(D.    ROSCHANSKY2). 

If  the  amplitude  curve  is  a  straight  line  the  amplitude  A  at  any  time  t 
can  be  obtained  from 

A  =  A 

in  which  A0  is  the  initial  amplitude  and  a  is  the  "lineal  decrement"  which 
determines  the  decrease  in  amplitude  just  as  d,  the  logarithmic  decrement, 
does  for  the  exponential  curves. 


K 

0.25 
0.20- 
0.15 

31 

i 

^n 

L 

^\ 

* 

»/ 

\ 

X 

X.. 

/ 

f> 

\ 

"N, 

X 

/ 

^ 

15 

N 

X 

/ 

-N 

/ 
/ 

^ 

/ 

/ 

X 

/ 

0.10 
0.05 

w 

^• 

^^ 

\ 

V 

x 

X 

^ 

\ 

N 

2-  ' 

^' 

X 

X 

s 

_a-— 

--&''' 

' 

\ 

*7 

X 

3- 

_-0_- 

-u-- 

\" 

*x 

N 

Time- 


FIG.   17. 


6.  If  the  amplitude  differs  from  the  exponential  form,  this  is  evidence 
of  the  fact  that  the  conditions  for  the  absorption  of  energy  in  the  spark 
are  not  the  same  as  for  absorption  due  to  ohmic  resistance,  but  are 
similar  to  those  in  an  electric  arc  (A.  HEYDWEiLLER12).  For  this  con- 
dition the  energy  Ag,  absorbed  per  second  in  terms  of  the  current  is 


Aa  =  al  +  b 


(1) 


(a  and  6  are  constants  for  the  particular  spark  gap  [Table  V])  which  for 
larger  currents  becomes 

A,  =  al  (2) 

But  since 

A    =  IV 


Vg  being  the  tension  across  the  gap,  it  follows  from  (2)  that  the  gap 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS  15 

voltage  remains  practically  constant  during  the  entire  series  of  os- 
cillations,* i.e., 

Vg  =  a  (3) 

c.  The  result  is  that  the  ratio  of  initial  to  final  amplitude  of  the 

A 

same  cycle  or  period,  -j—  >    and  hence  also  [Art.  86]  the  decrement,  do  not 

A-2 

remain  constant  for  all  cycles,  f  The  increase  of  the  decrement  is  shown 
by  the  curves  BI  and  B2  (Fig.  17)  for  the  successive  cycles  as  the  ampli- 
tudes AI  and  A  2  die  out.  In  short  no  one  definite  characteristic  decre- 
ment exists  for  the  entire  series  of  oscillations. 

Nor  can  a  definite  resistance  be  ascribed  to  the  spark  gap  for  those 
cases  in  which  the  energy  loss  is  not  proportional  to  72.  If  then  in 
practice,  an  equivalent  gap  resistance  or  simply  a  "gap  resistance"  Rg 
is  referred  to,  this  is  intended  to  mean  that  resistance  which,  if  sub- 
stituted for  the  gap,  would  absorb  the  same  amount  of  energy  as  is 
actually  absorbed  by  the  spark  gap  during  the  entire  oscillation  series 
following  the  same  amplitude  curve,  t 

If  the  condition  Va  =  a  applies,  and  we  have  a  straight-line  amplitude 
curve,  then 

Rg  =  —f-  (/o  being  the  initial  amplitude). 
"trl  o 

For  the  other  extreme,  when  the  energy  loss  in  the  circuit  due  to  resist- 
ance is  by  far  the  greater  and  the  curve  is  exponential  we  have  (H. 

BARKHAUSEN12) 

8a 


A  constant  gap  resistance  Rg  would  have  [Art.  8d]  a  corresponding 
"gap  decrement" 


dg  =  irRg  ^Jj~  (4) 

so  that  the  total  decrement  for  a  condenser  circuit  with  spark  gap  would 
be 

d  =  dj  +  dg 

As  this  value  of  the  decrement  is  constant  for  the  entire  series  of  oscilla- 

*  This,  however,  does  not  hold  during  a  single  half  period,  but  is  approximately 
correct  if  Vg  be  considered  as  the  average  value  of  the  gap  voltage  for  a  half  period. 
Even  this  average  value  does  not  remain  absolutely  constant  for  the  entire  train  or 
series  of  oscillations,  but  gradually  increases  from  cycle  to  cycle  for  copper  and  silver 
electrodes  and  gradually  decreases  with  magnesium  electrodes  (D.  RoscHANSKY2). 

t  For  the  extreme  case,  in  which  the  energy  lost  in  the  gap  is  the  determining  factor 
and  the  amplitude  curve  is  a  straight  line,  we  have  the  difference  of  A\  and  Az,  instead 
of  their  ratio,  constant. 

%i.e.,  RgI2eff  [Art.  44]  is  the  average  energy  actually  absorbed  by  the  spark  gap 
during  1  second.13 


16 


WIRELESS  TELEGRAPHY 


To  Induction  Coil 

F, 


tions,  it  does  not  properly  characterize  the  decrease  in  amplitude  from 
cycle  to  cycle,  but  is  the  average  value  of  the  gradually  increasing  dec- 
rement, its  use  in  practice  being  very  convenient  for  the  qualitative  con- 
sideration of  condenser  circuits  having  a  spark  gap  and  corresponding 
approximately  to  the  single  and  definite  decrement  which  is  a  precise 
and  sufficient  characterization  of  the  time-decrease  of  the  amplitude 
for  condenser  circuits  having  no  gap. 

d.  Aside  from  the  change  in  form  of  the  amplitude  curve  caused  by 
the  spark,  it  has  been  observed  that  in  a  condenser  circuit  with  gap 
the  oscillations  may  abruptly  cease  as  soon  as  the  amplitude  has  fallen 
to  a  more  or  less  small  fraction  of  the  initial  amplitude. 

10.  Methods    for    Determining    the    Spark    Gap    Damping. — Two 

methods   have   in   general   been   used    for 
measuring  the  gap  damping  and  resistance. 

a.  The  first  of  these,  the  so-called  reson- 
ance method,  is  based  on  a  procedure   for 
determining  the  total  decrement,  which  will 
be  considered  in  detail  later  [Art.  74,  etc.]. 

\R  The  total  decrement  is  first  measured  with 
and  then  without  the  spark  gap  [Art.  78c]; 
the  difference  of  the  two  values  obtained 
is  then  the  gap  decrement  dg,  from  which 
the  gap  resistance,  Rg  [see  equation  (4)  Art. 
9]  can  also  be  determined. 

b.  The     second14     is    the     substitution 
method.     In    Fig.   18,  F  is  the  spark   gap 

whose  resistance  is  to  be  measured,  A  is  a  hot-wire  ammeter  and  R  is 
a  very  high  ohmic  resistance  (or  self-inductance)  through  which  the 
condenser,  C,  can  be  charged  in  spite  of  the  gap,  but  sufficiently  high 
so  as  not  to  appreciably  affect  the  oscillations  passing  through  F.  First 
the  indication  of  A  is  noted  with  F  in  circuit.  Then  a  variable  non- 
inductive  resistance  is  substituted  for  F  and  is  adjusted  until  A  has  the 
same  indication  as  before.  The  spark-gap  resistance  is  then  the  same  as 
the  substituted  resistance,  if  the  coefficient  of  self-induction  of  the 
condenser  circuit,  the  discharge  frequency  and  the  spark  gap  FI  have 
been  held  constant  in  both  cases  [see  Art.  lie,  2]. 

11.  The  Factors  which  Determine  the  Amount  of  Gap  Damping.15 — 
a.  Relation  to  the  Current  Amplitude. 

The  gap  resistance,  other  things  being  equal,  and  particularly  for  the 
same  gap  length,  varies  inversely  with  the  current  amplitude.  Within 
the  limits  encountered  in  .wireless  telegraph  practice  the  relation 

«-«  T.  <» 

between  gap  resistance  and  current  amplitude  is  approximately  accurate. 


FIG.  18. 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS  17 

Assuming  that  the  circuit  contains  only  a  single  spark  gap  of  constant 
length,  the  voltage  amplitude  must  remain  constant.  If  then  the 
current  amplitude  is  varied  by  changing  the  coefficient  of  self-induction 
of  the  circuit,  then  it  follows  from  (1)  that 


If,  on  the  other  hand,  the  self-induction  is  kept  constant  and  the  current 
varied  by  changing  the  capacity,  we  have 

I      t!6] 


Thus  an  increase  in  the  self-induction  of  the  circuit  as  in  the  first  case 
causes  an  increase  in  the  gap  resistance,  while  an  increase  in  the  capacity 
reduces  the  gap  resistance. 

It  follows  that  within  the  limits  for  which.  the  relation  (1)  holds,  the 
spark-gap  decrement  is  practically  independent  of  the 
capacity  and  self-induction  of  the  circuit,  being  de- 
termined only  by  the  gap  itself. 

b.  The  gap  resistance  and  decrement  are  however 
not  independent  of  the  resistance  of  the  circuit,  both 
increasing  for  an  increase  of  the  circuit  resistance. 

c.  The  effect  of  the  gap  itself  upon  the  gap  resis- 
tance depends  upon: 

1.  The  material  of  the  electrodes. 

2.  The  form  of  the  gap,  and  if  the  electrodes  are 
spheres,  upon  the  radius  of  these. 

3.  The  gas  or  medium  through  which  the  spark  passes,  and 

4.  The  length  of  the  spark. 

As  to  the  material  of  which  the  electrodes  are  made,  it  has  been 
found  that  copper  and  silver  cause  a  very  high,  magnesium,  tin  and  zinc, 
a  very  low  resistance,  while  aluminium  stands  between  these  groups. 

The  radius  of  spherical  electrodes,  particularly  for  long  sparks, 
greatly  affects  the  gap  decrement;  the  latter  is  much  smaller  with  balls 
of  large  radius  than  for  small  spheres,  the  gap  length  being  the  same 
throughout.  For  disc-shaped  electrodes  the  decrement  is  practically 
the  same  as  for  spheres  of  very  large  radius. 

If  the  gap  medium  is  hydrogen,  a  very  high  decrement  is  obtained,  it 
being  less  with  illuminating  gas,  carbon  dioxide,  air,  oxygen  and  par- 
ticularly low  for  sulphur  dioxide. 

For  the  same  electrodes,  i.e.,  of  a  given  material  and  radius  and  for 
a  given  gas  in  the  gap,  the  decrement  becomes  larger  as  the  discharge 
voltage  becomes  smaller  for  a  gap  of  constant  length;  or,  again,  with 
constant  voltage  the  gap  decrement  becomes  smaller  as  the  gap  is 
shortened. 


18 


WIRELESS  TELEGRAPHY 


d.  For  the  relation  between  the  gap  decrement  and  the  gap  length 
the  substitution  method  [Art.  106]  gives  curves  similar  to  B*  in  Fig. 
19,  if  the  length  F  in  Fig.  18  is  varied  without  changing  the  rest  of  the 
circuit;  the  increase  in  gap  resistance  with  increasing  length  is  at  first 
very  gradual,  then  quite  rapid.  If  the  gap  decrement  is  determined 
directly  by  the  resonance  method  [Art.  10a]  for  different  gap  lengths,  a 
curve  of  the  form  of  A*  in  Fig.  19  is  obtained.  Here  we  have  the  gap 
decrement  first  rapidly  and  then  more  slowly,  falling  off  as  the  gap  length 
is  increased.  The  curve  determined  by  M.  WiEN17  with  spherical  zinc 
electrodes  is  shown  in  Fig.  20.  f 

The  following  explanation  accounts  for  this  difference  in  the  results 


0.06 


0.05 


0.04 


0.03 


0.01 


\ 


0.5 


\ 


1.5 


10\     11     lt\    13  \U  x  10*  Volts 


15 

FIG.  20. 


Gap  Length 
in  Cm. 


obtained.  In  the  resonance  method  giving  curve  A,  the  gap  under  in- 
vestigation is  the  only  gap  in  the  circuit  and  its  length  determines  the 
voltage  and  current  amplitudes.  Hence  as  the  gap  length  is  varied  the 
current  is  correspondingly  changed  and  the  gap  resistance  is  determined 
for  a  different  current  amplitude  with  each  observation.  An  increase  in 
the  gap  length  alone  would  cause  an  increase  in  gap  resistance,  but  an 

*  Abscissae  <*  gap  length,  ordinates   <*  gap  resistance. 

f  The  values  given  are  for  the  following  condenser  circuits: 

Radius  of  Electrodes                     C  L 

Circles       O                    220mm.  4.25  X  10~4MF.  40,900  C.G.S.  Units 

Crosses     X                       50  mm.  4.25  X  10~4MF.  40,900  C.G.S.  Units 

Dots                                  50mm.  6.3    X  10~4MF.  40,500  C.G.S.  Units 

Circles  with  dots       G     50mm.  5.8    X  10~3MF.  40,500  C.G.S.  Units 

Squares      D                     50mm.  5.8    X  10~WF.  7,300  C.G.S.  Units 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS 


19 


increased  gap  length  also  means  increased  current  amplitude,  which  latter 
decreases  the  gap  resistance.  We  therefore  have  two  factors  with  opposite 
tendencies;  with  short  gaps  the  action  of  the  current  amplitude  is  the  more 
effective  of  the  two,  but  as  the  gap  becomes  longer  it  is  partly  compen- 
sated by  the  effect  of  the  greatly  increased  gap  length. 

In  the  substitution  method  (Fig.  18),  current  and  voltage  are  deter- 
mined by  the  length  of  the  gap  FI,  and  therefore  practically  independent 
of  the  gap  Fj  whose  resistance  is  to  be  measured.  Hence  as  the  length 
of  F  is  varied  the  current  amplitude  remains  practically  constant. 

In  addition  there  is  an  essential  difference  in  the  nature  of  the  two 
methods.  In  the  substitution  method  we  find  that  resistance  which, 
when  put  in  place  of  the  spark  gap,  produces  the  same  c'urrent  effect 
[Art.  43a].  The  resonance  method  gives  that  value  of  the  resistance 


1       2       3^       5       6       78       9      10     11     12    13    U     15 
Length  of  Gap  F  in  mm 

FIG.  21. 

which,  when  replacing  the  spark  gap  produces  the  same  degree  or  rather 
sharpness  of  resonance  in  a  loosely  coupled  secondary  circuit  [Art.  64c.] 
These  two  are  not  necessarily  identical. 

e.  From  a  and  b  the  following  conclusions  in  regard  to  the  substitution 
method  may  be  drawn: 

1.  The  gap  resistance  of  F  (Fig.  18)  is  dependent  not  only  upon  its 
dimensions,  the  capacity  and  the  self-induction  of  the  circuit,  but  also 
upon  the  length  of  the  gap  FI  (Fig.  18)  upon  which  the  current  ampli- 
tude depends.  How  great  this  effect  is  may  be  seen  from  Fig.  21,  in 
which  the  gap  resistance  of  F  is  shown  for  several  different  lengths  of  FI.IB 
Any  statement  of  the  resistance  of  F  without  an  accompanying  statement 
of  the  dimensions  of  FI  is  therefore  just  as  useless  as  stating  that  the 
resistance  of  a  metallic  filament  incandescent  lamp  is  so  and  so  without 
mentioning  the  voltage  or  current  at  which  the  measurement  was  made. 


20  WIRELESS  TELEGRAPHY 

2.  Results  obtained  by  the  substitution  method  must  not  be  con- 
sidered as  conclusive  in  case  there  is  only  a  single  spark  gap  in  the  con- 
denser circuit.  For  when  FI,  having  a  larger  resistance,  is  in  the  circuit, 
thi s  has  a  considerable  effect  on  the  resistance  of  F.  Furthermore  the  form 
of  the  amplitude  curve  and  the  conditions  in  the  gap  FI  must  be  some- 
what influenced  by  placing  an  ohmic  resistance  as  a  substitute  for  the 
gap  F,  so  that  it  does  not  follow  from  the  fact  that  the  current  effect 
is  the  same  in  both  cases,  that  the  energy  absorbed  at  F  is  also  the 
same.19 

12.  Spark  Gaps  in  Series  (Multiple  Gaps). — If  a  number  of  spark 
gaps  are  connected  in  series  in  the  same  condenser  circuit  the  interesting 
question  arises:  Is  the  decrement  for  the  several  gaps  in  series  greater 
or  less  than  that  obtained  for  a  single  spark  gap  with  the  same  initial 
voltage?     Investigations20  intended  to  answer  this  question  have  shown 
that  up  to  potentials  of  about  80,000  volts  and  down  to  capacities  as 
low  as  0.6  X  10~3  M.F.  the  series  gap  has  a  higher  decrement  than  the 
simple  gap. 

13.  Energy   Losses   in   the   Dielectric   of   the   Condensers.21 — The 
alternating  field  produced  in  the  insulating  material  (dielectric)  between 
the  coatings  of  the  condensers  by  the  oscillations,  involves  an  energy 
loss  for  practically  all  insulators.     It  is  due  to  the  so-called  "  dielectric 
hysteresis"  which  is  the  electrical  analogue  of  magnetic  hysteresis. 

a.  Such  investigations  as  have  been  made  so  far  with  various  materials 
indicate  that,  independently  of  the  frequency  of  the  oscillations,  the 
energy  absorbed  per  cycle  in  the  condenser  is  proportional  to  the  total 
energy  in  the  condenser  during  that  period.  Hence  the  "hysteresis 
decrement,"  dh,  i.e.,  that  portion  of  the  total  decrement  due  to  the  di- 
electric hysteresis  losses,  is  independent  of  the  frequency  of  the  oscilla- 
tions or  the  dimensions  and  capacity  of  the  condenser,  and  is  deter- 
mined solely  by  the  dielectric  material,  that  is  by: 

1.  Its  chemical  composition, 

2.  Its  temperature. 

As  to  the  kind  of  material,  it  has  been  found  that  the  hysteresis 
decrement  is  not  appreciable  for  air,  very  small  for  well  dried  paraffin 
oil  and  transformer  oil  (dh  =  0.001  —  0.002),  also  for  good  flint  glass* 
(dh  =  0.006  —  0.01)  and  somewhat  greater  for  certain  grades  of  hard 
rubber.  It  may  run  very  high  for  certain  kinds  of  glass,  e.g.,  ordinary 
window  glass,  other  grades  of  hard  rubber,  mica  and  the  otherwise  very 
convenient  insulating  material,  micanite. 

Increasing  the  temperature  causes  an  increase  in  the  hysteresis 
decrement,  at  times  in  fact  a  very  considerable  increase. 

*  Can  be  obtained  from  Molineaux,  Webb  &  Co.,  of  Manchester  (Ancoats,  Kirby 
Str.)  and  the  glassworks  at  Ehrenfeld  near  Cologne. 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS  21 

b.  With  certain  materials  the  hysteresis  decrement  depends  upon 
the  energy  load,  We,  the  relation  being  of  the  form 

dh  =  a  +  fiW  e* 
for  some  materials,  and  for  others 

dh  =  aWf 

where  a  and  (3  are  constants  for  the  particular  material.  In  some 
cases  this  effect  of  the  energy  load  is  only  an  indirect  one;  due  to  the 
increased  amplitude  of  the  oscillations  and  the  consequent  increase  in 
the  energy  absorbed,  a  higher  temperature  is  produced,  which  in  turn  in- 
creases the  hysteresis  decrement. 

14.  Energy  Lost  by  Leakage  Discharge. — a.  For  our  purposes  it  is 
necessary  to  distinguish  between  leakage  of  two  kinds.     The  first  of 


FIG.  22. 

these22  occurs  whether  the  conductor  is  charged  by  oscillations  or  has  a 
static  charge.  It  consists  of  the  well-known  phenomenon  of  fine  brush 
discharges  emanating  from  conductors  charged  to  a  very  high  potential, 
particularly  from  edges  or  points.  This  is  due  to  the  fact  that  under  the 
influence  of  the  strong  electric  field  the  air  becomes  a  conductor  (ionized) 
and  hence  a  part  of  the  charge  is  led  off.  This  phenomenon  is  observed 
very  frequently  on  influence  machines  and  occasionally  in  the  air  con- 
densers used  in  wireless  telegraphy,  wherever  the  plates  have  uneven 
surfaces  or  along  their  edges;  especially  also  on  antennae  or  coils  charged 
to  a  high  potential. 

*  The   "  energy  load,"    We,   is  the  maximum   energy  contained    per  cc.  of  the 
dielectric  material.     It  is 


where  k  =  ratio  of  the  dielectric  constant  of  the  material  to  that  of  air  and  E  = 
strength  of  the  electric  field. 


22  WIRELESS  TELEGRAPHY 

The  second  kind  of  leakage  discharge  occurs  only  with  oscillations; 
it  appears  at  the  moment  when  the  oscillation  commences,  continuing 
even  if  the  conducting  elements  in  question  do  not  have  their  potential 
increased  during  the  remainder  of  the  oscillation.  A  leakage  discharge 
of  this  nature  is  observed  in  Ley  den  jars  (see  photographic  reproduction 
in  Fig.  22)  or  other  condensers  having  a  solid  dielectric.  It  is  char- 
acterized by  long,  fine,  branching  rays  which  spread  out  over  the  surface 
of  the  dielectric  from  the  edge  of  the  condenser  coatings. 

6.  The  essential  requirement  for  a  noticeable  leakage  discharge  in 
both  cases  is  a  sufficient  ionization  of  the  air,  which  in  turn  means  a 
sufficiently  strong  electric  field.  If  sharp  edges  and  points,  at  which 
the  field  strength  assumes  especially  great  intensities,  are  avoided  as 
much  as  possible,  these  discharges  need  not  be  feared,  as  long  as  the 
potential  is  kept  within  a  few  hundred  volts. 

c.  When,  however,  a  discharge  as  just  described,  occurs,  it  means 
an  actual  loss  of  energy  in  any  case.  How  great  this  loss  may  become  is 
not  known.  But  what  has  been  definitely  determined  is  that  if  Leyden 
jars  are  properly  constructed  the  increase  in  the  decrement  due  to  this 
energy  loss  can  be  kept  below  0.002  for  a  voltage  amplitude  of  30,000 
volts,  and  below  0.007  for  40,000  volts  [Art.  86]. 

In  addition  it  has  been  found  that  a  discharge  of  the  second  kind  has  a 
tendency  to  produce  a  fluctuation  in  the  frequency  [Art.  79]. 

15.  Energy  Lost  by  Eddy  Currents. — The  alternating  magnetic  field 
produced  by  the  oscillations  in  a  condenser  circuit  induces  so-called 
"eddy  currents"  in  all  conductors  through  which  the  lines  of  magnetic 
flux  pass.  The  energy  which  these  currents  dissipate  in  the  form  of  heat, 
other  things  being  equal,  is  much  greater  for  the  high  frequencies  used 
in  wireless  telegraphy  than  for  the  lower  frequencies  customary  in  com- 
mercial power  and  lighting  circuits.  Being  a  direct  loss  to  the  total 
energy  of  the  condenser  circuit,  it  causes  a  corresponding  increase  in  the 
damping. 

All  conductors  in  the  immediate  vicinity  of  the  condenser  circuit, 
particularly  those  conductors  (such  as  terminals)  which  are  inside  of 
coils  where  the  magnetic  field  is  concentrated,  are  subject  to  eddy 
currents.  Very  dangerous  in  this  respect  are  the  coatings  of  condensers 
which,  in  view  of  their  extensive  surface  and  thinness,*  may  cause  con- 
siderable eddy  current  losses.  Leyden  jars  are  very  troublesome  on  this 
account;  with  plate  condensers  it  is  much  easier  to  place  the  coatings  in 
such  a  position  as  to  minimize  the  magnetic  flux  cut  by  them. 

Care  should  be  taken  in  using  such  artificial  insulating  materials  as 
are  frequently  substituted  for  hard  rubber  or  marble,  if  placed  in  a  strong 
high  frequency  magnetic  field.  The  conductivity  of  such  substances  may 
be  great  enough  to  cause  considerable  energy  losses.23 

*  Very  thick  masses  of  metal  are  less  dangerous. 


NATURAL  OSCILLATIONS  OF  CONDENSER  CIRCUITS  23 

16.  Relative  Importance  of  the  Various  Energy  Losses. — a.  Con- 
denser Circuits  with  Spark  Gap. — The  important  question  here  is:  Which 
energy  losses  come  into  consideration  as  compared  to  the  energy  dissi- 
pated in  the  spark? 

If  the  conductors  of  the  circuit  are  copper  wires  or  tubes  of  sufficient 
diameter,  it  is  safe  to  conclude  that  the  Joulean  (heat)  decrement  will  be 
entirely  negligible  as  compared  to  the  spark  gap  decrement. 

Eddy  current  losses  may  become  very  considerable  if  provoked  by 
clumsy  connections  or  arrangements,  particularly  with  the  condensers. 
With  proper  care,  however,  these  losses  may  also  be  so  reduced  as  to  have 
no  material  effect  on  the  total  decrement. 

In  view  of  the  high  potentials  for  which  condenser  circuits  with  spark 
gaps  are  usually  designed,  a  dielectric  of  high  insulating  quality  is 
essential.  If,  then,  compressed  air  condensers  [Art.  396]  or  condensers 
filled  with  a  good  oil  are  used,  the  hysteresis  decrement  becomes  negligible 
as  compared  to  the  gap  decrement.  The  hysteresis  losses  in  good  flint 
glass  are  also  much  smaller  than  in  the  spark  gap.  As  soon  as  other 
dielectrics  are  tried,  however,  losses  comparable  to  or  even  greater  than 
those  occurring  in  the  spark  gap  must  be  anticipated,  especially  if  the 
condensers  are  to  be  highly  charged. 

The  energy  lost  by  leakage  discharge  in  condensers  can,  by  careful 
design,  be  reduced  to  a  quantity  negligible  in  comparison  to  the  gap 
losses.  In  any  case  this  loss  is,  in  general,  far  less  important  than  that 
caused  by  the  frequency  fluctuations  [Art.  86]. 

6.  Condenser  circuits  without  a  spark  gap  are  usually  designed  for 
comparatively  low  voltages.  For  that  case,  losses  due  to  leakage  dis- 
charges usually  disappear.  Furthermore,  as  air  condensers — even  at 
atmospheric  pressure — can  generally  be  used,  losses  due  to  dielectric 
hysteresis  can  be  entirely  avoided.  If,  however,  such  potentials  as  may 
be  encountered  do  produce  leakage  discharges,  the  losses  may  be  far 
greater  than  those  due  to  Joulean  heat. 

The  latter  may  be  greatly  reduced  by  the  use  of  sufficiently  thick  and 
massive  copper  wires  or,  better  yet,  copper  bands  or  strips,  and  especially 
by  properly  wound  braided  wire  consisting  of  individually  insulated 
conductors  [Art.  36d].  This,  however,  tends  to  increase  the  eddy  current 
losses,  and  if  these  losses  are  not  minimized  by  the  greatest  care,  it  is 
not  possible  to  bring  the  decrement  below  0.01.  In  fact,  decrements  of 
about  0.003  are  the  very  lowest  attained  in  practice. 


CHAPTER    II24 
OPEN   OSCILLATORS 

In  a  condenser  circuit,  the  condenser  itself  offers  the  only  break  in  the 
continuity  of  the  circuit.  It  is  therefore  usually  referred  to  as  a  "closed 
oscillator"  or  "closed  oscillating  circuit,"  as  distinct  from  systems  in 
which  the  metallic  conductor  is  not  even  approximately  continuous  and 
which  are  therefore  "open  oscillators." 

1.  THE  LINEAL  OSCILLATOR 

17.  The    Fundamental    and    Upper    Harmonic    Oscillations. — The 

simplest  form  of  open  oscillator  is  the  straight  lineal  oscillator,  i.e.j  a 
straight  metal  wire  or  rod.  If  its  two  halves  are  given  a  positive  and 
a  negative  charge  respectively  until  a  sufficiently  high  potential  is 
reached,  so  that  a  spark  discharge  passes  between  the  two  halves  (at 


To  Induction  Coil 
FlG.   23. 

Fj  Fig.  23),  an  electromagnetic  oscillation  takes  place  here  just  as  in  a 
condenser  circuit.* 

In  general  this  oscillation  is  not  a  simple  one,  but  is  made  up  of  a 
number  of  component  oscillations  of  different  frequencies,  different 
current  and  voltage  distributions  and  different  electric  and  magnetic 
fields.  It  will  therefore  be  necessary  to  consider  separately  the  so-called 
"fundamental  oscillation" — that  having  the  lowest  frequency,  as  in 
acoustics — and  its  "upper  harmonics"  or  "upper  partial  oscillations." 
This  subdivision  in  the  treatment  is  further  justified  by  the  fact  that 
each  of  these  oscillations  can  be  produced  independently  of  the  others. 

18.  Current  and  Potential  Distribution  in  the  Fundamental  Oscilla- 
tion.— a.  In  a  condenser  circuit,  as  used  in  practice,  the  quantity  of 

*  The  natural  oscillation  can  be  induced  in  open  oscillators  as  well  as  in  condenser 
circuits  without  the  existence  of  a  spark  gap  in  the  oscillator  [Art.  109]. 

24 


OPEN  OSCILLATORS 


25 


electricity  passing  through  a  cross-section  of  the  circuit  in  a  certain 
length  of  time,  just  as  in  ordinary  direct-current  circuits,  is  practically 
the  same  at  all  points,*  i.e.,  the  currentf  has  the  same  phase  and  ampli- 
tude throughout  the  entire  circuit.  We  can  therefore  speak  of  a  definite 
phase  and  amplitude  of  the  current  just  as  for  the  alternating  currents 
used  in  power  and  lighting  circuits. 

In  a  lineal  oscillator  the  current  f  may  also  be  considered  as  having 
the  same  phase  at  all  parts  of  the  oscillator.  But  the  current  amplitude 
is  entirely  different  at  different  parts  of  the  oscillator.  If  a  curve  be  plotted 


FIG.  24. 

giving  the  current  amplitude  at  each  point  of  the  oscillator  as  ordinates, 
this  "curve  of  current  distribution " J  is  found  to  be  an  approximate 
sine  curve  (dotted  line  in  Fig.  23).  The  current  amplitude  is  greatest 
at  the  middle  and  zero  at  the  ends  of  the  oscillator.  In  other  words, 
there  are  "current  nodes"  at  each  end  and  a  "current  anti-node"  at  the 
middle. 

6.  Correspondingly,  if   we   plot   the   electric   charge   or  rather   the 
potential  values   along  the   length   of   the   oscillator,    we   obtain   the 


FIG.  25. 

"curve  of  potential  distribution"  as  shown  in  Fig.  23  by  the  full  line 
(sinusoidal)  V.  It  should  be  noted  that  "potential"  or  "voltage  anti- 
nodes  "  occur  at  each  end  of  the  oscillator,  the  "  potential  node  "  being 
at  the  middle. 

*  Hence  called  a  "quasi-stationary  current."    Compare  footnote  in  Art.  24c. 

f  The  current  =  quantity  of  electricity  passing  through  a  cross-section  of  the 
circuit  in  1  second. 

t  This  should  not  be  confused  with  the  " current  curve"  of  Art.  16,  which  gives 
the  variation  with  time. 


26  WIRELESS  TELEGRAPHY 

c.  Just  as  in  a  condenser  circuit,  and  for  the  same  reasons,  the  current 
and  voltage  in  an  open  oscillator  have  a  90°  phase  displacement.  The 
distribution  curves  of  the  current  and  the  voltage  are  shown  in  Figs.  24 
and  25  respectively  for  successive  eighths  of  a  cycle,  curves  bearing  the 
same  number  in  the  two  figures  being  for  the  same  instant. 

19.  Frequency  of  the  Fundamental  Oscillation.  —  The  simplest  way 
to  arrive  at  the  fundamental  frequency  is  by  the  following  consideration  : 

a.  The  current  and  potential  distribution  curves  of  Fig.  23  are  of  the 
same  type  as  the  so-called  "stationary  waves"  encountered  in  other 
physical  phenomena   (as  in  acoustics).     Such  stationary  waves  result 
when  two  advancing  waves  of  the  same  amplitude  and  frequency  but  of 
opposite    direction    occur    simultaneously.     The    wave-length    of    the 
stationary  wave  is  then  the  same  as  that  of  the  advancing  waves,  if  by 
wave-length  of  the  stationary  wave  we  understand  twice  the  distance 
between  two  consecutive  nodes  or  anti-nodes. 

As  is  well  known,  the  "wave-length,"  X,  of  an  advancing  wave  is 
equal  to  the  distance  traveled  by  the  wave  in  one  complete  cycle.  The 
propagation  velocity,  VL,  is  the  distance  traveled  in  1  second.  If 
the  duration  of  a  cycle  or  period  is  T  seconds,  then  I/  T  or  N  complete 
cycles  occur  per  second.  Hence  we  have  the  relation 

VL  =  N\=*  (1) 

b.  As  we  are  j  ustified  in  considering  the  oscillations  of  a  lineal  oscillator, 
as  shown  in  Fig.  23,  as  stationary  waves,  we  can  apply  equation  (1),  writ- 
ing it  in  the  form 

N  =  ^  (2) 

N  being  the  frequency. 

From  a  and  as  shown  in  Fig.  23,  one-half  the  wave-length  is  equal  to 
the  total  length,  I,  of  the  oscillator,  i.e., 


c.  The  velocity  of  propagation  of  the  electromagnetic  waves  occurring 
in  air  along  a  conductor25  is  practically  equal  to  the  velocity  of  light  in 
air,  hence: 

VL  =  3  X  1010  cm./sec. 
whence:  Ar  _  3  X  1010cm./sec.  .  , 

~2lU.)  ~ 
This  simple  relation  if  not  quite  accurate  is  approximately  correct.* 

*  This  and  what  follows  is  based  on  the  assumption  that  the  oscillator  is  in  free. 
space,  i.e.,  for  practical  consideration,  its  distance  from  conductors  or  high  insulation 
must  be  large  in  comparison  to  its  own  dimensions. 


OPEN  OSCILLATORS 


27 


20.  The  Electromagnetic  Field  of  the  Fundamental  Oscillation. — 

a.  Direction  of   the  Electromagnetic  Field. — The  magnetic  field   is  com- 
paratively simple,  the  lines  of  induction  being  circles  whose  axes  coincide 


FIG.  26. 


with  the  axis  of  the  oscillator.     Fig.  26*  shows  the  lines  of  induction  in 
the  equatorial  plane |  at  a  given  instant. 

The  lines  of  force  of  the  electric  field  are  shown  in  Figs.  27  to  30,  for 
undamped  oscillations!)!  at  each  eighth  period  during  one-half  a  cycle 


as  calculated  by  M.  ABRAHAM26  and  drawn  by  F.  HACK26.     Fig.  27  repre- 
sents the  moment  at  which  the  charge  of  the  oscillator  is  zero,  while 

*  This  and  the  following  figures  do  not  indicate  the  falling  in  amplitude  with 
distance  [r,  d]. 

f  That  is,  the  plane  perpendicular  to  the  oscillator  at  its  middle. 

|  For  damped  oscillations  the  nature  of  the  phenomenon  would  not  be  notice- 
ably different.27 


28 


WIRELESS  TELEGRAPHY 


the  current  is  a  maximum;  the  following  figures  show  conditions  at  each 
successive  eighth  period  until  after  Fig.  30,  Fig.  27  would  again  apply 
but  with  opposite  signs,  and  so  on. 


To  better  comprehend  these  figures  consider  first  that  at  the  moment 
of  zero  charge,  as  in  Fig.  27,  no  lines  of  force  emanate  from  the  oscillator. 
Immediately  thereafter,  however,  the  oscillator  becomes  charged,  for 


example  as  in  Fig.  28,  the  upper  half  positively,  the  lower  part  negatively, 
and  lines  of  force  emanating  from  the  upper  half  reenter  in  the  lower 
half.  This  process  continues  cumulatively  until  the  maximum  charge 


OPEN  OSCILLATORS 


29 


is  reached  at  the  end  of  the  quarter  period  (Fig.  29) .  Then  the  lines  of 
force  in  the  oscillator  gradually  decrease  again  until  zero  is  reached  after 
half  a  period.  A  part  of  the  lines  of  force  which  have  emanated  from 
the  oscillator  (Fig.  30)  during  the  first  quarter  period  go  through  a 
peculiar  contraction  during  the  second  quarter,  assuming  a  kidney-like 
shape,  and  at  the  same  time  continue  to  move  farther  away  from  the 
oscillator.  What  happens  to  them  as  they  pass  off  into  distance  is 
shown  in  Figs.  295  and  296,  the  first  representing  conditions  at  the 
moment  of  maximum  charge,  the  second  at  zero  charge.  The  advanc- 
ing lines  of  force  gradually  become  arcs  of  circles. 

b.  Phase  of  the  Electromagnetic  Field.  Advancing  Waves. — Neither 
the  magnetic  nor  the  electric  field  has  the  same  phase  at  any  moment 
throughout  the  entire  space  affected.  Both  assume  the  form  of  a 
wave  advancing  out  from  the  oscillator  with  the  velocity  of  light. 

The  following  will  explain  what  is  understood  by  an  advancing 
electromagnetic  wave,  in  the  simplest  case,  when  the  amplitude  remains 
constant.  If  over  each  point  of  the  line  of  direction  (OX  in  Fig.  31) 


C\ 


FIG.  31. 

of  the  advancing  wave  we  were  to  plot  as  ordinates  the  field  intensity 
at  any  given  moment,  a  sine  curve,  such  as  the  full  line  curve  in  Fig. 
31,  would  result.  It  represents  the  distribution  of  the  field  strength 
along  OX  at  this  moment.  A  moment  later  a  similar  sine  curve  is  ob- 
tained, but  slightly  displaced  from  the  first  one  in  the  direction  of  the 
advancing  wave  front  (as  shown  by  the  arrow).  This  is  indicated  in 
Fig.  31  by  the  dotted  line  curve.  Hence  a  conception  of  the  process 
may  be  formed  by  considering  the  sine  curve  to  move  in  the  direction  of 
and  with  the  velocity  of  the  advancing  wave,  its  position  at  any  instant 
indicating  the  distribution  of  the  field  intensity  at  that  moment. 

From  the  preceding,  it  follows  that  at  any  one  point  there  exists  a 
simple  alternating  field  whose  frequency  is 

VL 
\ 


N  = 


in  which  X  is  the  wave-length  of  the  advancing  wave  and  VL  its  velocity, 
in  this  case  the  velocity  of  light. 


30  WIRELESS  TELEGRAPHY 

It  is  evident  that  the  phase  varies  from  point  to  point.*  It  is  the 
same,  however,  for  two  points  lying  in  the  direction  of  the  advancing 
wave  and  separated  by  the  distance  of  one  wave-length,  or  a  multiple 
thereof.  If  the  two  points  are  just  a  half  wave-length  apart,  the  phase 
difference  will  be  180°.  Or,  in  general,  we  have  the  phase  difference  is 

2Trx       360°.z     ,  .    ,,      ,.  , 

_  — —  where  x  is  the  distance  between  the  two  points. 

A  A 

Similarly,  if  x  is  the  difference  in  the  respective  distances  of  two 
points  in  the  equatorial  plane  from  the  oscillator,  the  phase  difference 

between  the  fields  at  these  points  is  also  -r— . 

A 

c.  The  Amplitude  of  the  Field. — Neither  the  amplitude  of  the 
magnetic  nor  that  of  the  electric  wave  remains  constant  for  different 
distances,  r,  from  the  oscillator;  the  amplitudes  decrease  as  r  increases. 
The  magnetic  wave  amplitude  in  the  immediate  proximity  of  the 
oscillator  roughly  <x  1/r2,  and  at  very  great  distances!  a  1/r;  the  elec- 
tric field  amplitude  also  oc  1/r  at  very  great  distances,  but  close  to  the 
oscillator  it  approximately  cc  1/r3. 

For  the  same  distance,  r,  from  the  oscillator,  the  amplitude  is  greatest 


FIG.  32. 

for  points  in  the  equatorial  plane;  for  any  points  outside  of  this  plane, 
it  decreases  as  the  distance  from  the  equatorial  plane  becomes  greater. 

d.  The  Field  at  Great  Distances  from  the  Oscillator. — The  electric 
as  well  as  the  magnetic  waves  approach  a  spherical  shape  (see  Figs.  295 
and  296)  as  the  distance  from  the  oscillator  becomes  very  great;  hence 
small  portions  of  the  wave  front  may  be  regarded  as  plane  waves.  In 
the  immediate  vicinity  of  the  equatorial  plane  the  lines  of  both  electric 
and  magnetic  flux  may  be  regarded  as  straight  lines,  the  electric  flux  lines 
being  perpendicular,  the  magnetic  lines  parallel  to  the  equatorial  plane 
(Fig.  32). 

The  electric  and  magnetic  fields  are  "in  phase "t  if  they  are  considered 
to  be  of  positive  value  in  the  directions  shown  by  the  arrows  in  Fig.  32. 

*  For  instance,  at  A  the  oscillation  shown  by  the  full  line  curve  (Fig.  31)  is  at 
that  instant  at  its  maximum,  whereas  a  moment  later,  as  shown  by  the  dotted 
curve,  it  has  already  decreased.  At  B,  on  the  other  hand,  there  is  an  increase  between 
these  two  instants. 

^  i.e..  the  distance  from  the  oscillator  is  "great"  or  "small"  in  relation  to  the 
wave-length. 

t  In  fact  synchronism  of  the  electric  and  magnetic  fields  exists  at  all  great  dis- 
tances from  the  oscillator  whether  in  or  outside  of  the  equatorial  plane. 


OPEN  OSCILLATORS  31 

If  EQ  and  Mo  are  the  amplitudes  of  the  electric  and  magnetic  fields 
respectively,  in  the  equatorial  plane  or  its  immediate  vicinity,  then  [see 
Art.  25c] 


in  which  |/0   is  the  current  amplitude  at  the  "  current  anti-node"  of  the 
oscillator. 

21.  Damping  of  the  Fundamental  Oscillation.  —  a.  Just  as  in  the  case 
of  condenser  circuits,  there  is  a  transfer  and  re-transfer  of  energy  between 
the  electric  and  magnetic  fields  in  the  oscillations  of  lineal  oscillators. 
There  is,  however,  one  very  important  difference.  In  a  condenser  circuit 
only  such  energy  as  is  in  some  way  changed  into  heat  (due  to  the  circuit 
resistance  or  in  the  dielectric  of  the  condenser)  is  lost.  But  in  a  lineal 
oscillator,  as  shown  in  Fig.  28  and  following  figures,  a  portion  of  the 
electromagnetic  field  together  with  the  energy  it  possesses  becomes 
severed  from  the  oscillator  and  passes  off  into  space.  The  energy  thus 
passed  off  is  therefore  lost  to  the  oscillator.  The  amount  of  energy  sent 
out  per  second  in  this  way  is  called  the  "radiation,"  2. 

b.  This  dissipation  of  energy  must  of  course  affect  the  damping  of  the 
oscillation,  so  that  to  the  other  decrements  there  is  added  a  "radiation 
decrement"  (also  called  the  "  HERTZ  decrement"). 

According  to  M.  ABRAHAM,26  the  radiation  decrement  of  a  lineal 
oscillator  is  given  by 

2.44 

d~  =  ~l 

log  nat  — 

(I  being  the  length,  r  the  radius  of  the  oscillator).     For  a  length  of  100 
meters,  d^  has  the  following  values  for  different  diameters  of  wire: 

Diam.  of  Wire  in  mm.  d2 

0.5  0.18 

1  0.20 

2  0.21 

3  0.22 

4  0.225 

5  0  .  23 

Hence  for  all  wires  within  these  limits  the  radiation  decrement  is  not  far 
from  0.2. 

c.  In  general,  the  radiation   decrement  is  much  greater  than  the 
Joulean  decrement,  assuming  the  oscillator  to  consist  of  copper  wire  of 
at  least  1  to  2  mm.  diam.     The  radiation  decrement  is  therefore  the 


32 


WIRELESS  TELEGRAPHY 


determining  factor  in  open  oscillators  which  have  no  spark  gap  and  no 
heavy  leakage  discharge. 

If  the  oscillator  contains  a  spark  gap,  the  gap  decrement  may  assume 
considerable  proportions,  just  as  in  condenser  circuits.  The  energy  loss 
due  to  leakage  (see  Art.  14a),  has  not  been  carefully  investigated  as  yet, 
though  it  has  been  found  at  times  to  be  quite  appreciable  as  compared 
with  the  other  losses. 

22.  Upper  Harmonics  of  the  Lineal  Oscillator. — a.  The  distribution 
of  current  and  potential  is  shown  for  the  first  3  harmonics  in  Figs.  33, 
34  and  35.  The  dotted  lines  marked  /  are  for  the  current,  the  full  lines, 
V,  for  the  potential. 


1st  Upper 
Harmonic 


FIG.  33. 


2nd  Upper 
^      Harmonic 


FIG.  34. 


3rd  Upper 
~7     Harmonic 


FIG.  35. 

6.  As  these  upper  harmonics  may  properly  be  considered  as  stationary 
waves  as  well  as  the  fundamental  oscillation,  we  have  the  following 
equations  for  wave-length  and  frequency: 

X  3  X  1010      1 

Fundamental:  ^  =  Z;    N  =  — x^ —  -  •  — 
2  2Lcm.       sec. 

v    *  TT  .      Xi       Z     A_        3  X  1010     1 

First  Upper  Harmonic:  -7.    =  o5  NI  =  — i — 

2        2  /cm.         sec. 

X2      Z  ,   3  X  1010     1 

Second  Upper  Harmonic:     ~  =  »;  7V2  =  3  -—7^ — 

^       o  2tcm.         sec. 

Hence  the  frequencies  of  the  upper  harmonics  are  simple  multiples  of  the 
fundamental  frequency. 

c.  The  conditions  for  the  electromagnetic  field  are  similar  to  those  of 
the  fundamental  oscillation.  Here  especially  we  have  a  portion  of  .the 
electric  lines  of  force  separating  and  passing  off  into  space.26  This  also 
results  in  a  continued  radiation  of  energy  with  the  consequent  radiation 
damping. 


OPEN  OSCILLATORS  33 

23.  Coils.28 — In  the  first  place  it  is  very  probable  that  natural  oscilla- 
tions of  the  kind  described  in  Art.  17,  et  seq.}  can  occur  in  a  wire  even  if  it 
is  wound  in  a  cylindrical  coil  instead  of  being  stretched  out  in  a  straight 
line. 

a.  The  current  and  potential  distribution  for  the  fundamental  and 
upper  harmonic  oscillations  is  qualitatively  the  same  as  for  straight  wires : 
the  fundamental  wave  has  a  current  anti-node  and  a  potential  node  at 
the  center  of  the  coil  and  current  nodes  with  potential  anti-nodes  at  either 
end,  while  the  first  upper  harmonic  has  current  nodes  and  potential 
anti-nodes  both  at  the  middle  and  at  the  ends.  Quantitatively,  however, 
the  relations  differ  in  several  respects  from  those  of  straight  wires. 

6.  Comparing  the  frequency  of  the  fundamental  oscillation  of  a  coil 
of  wire  with  that  of  a  lineal  oscillator  of  the  same  length  of  wire,  we  have 
the  following :  With  long,  narrow  coils  the  frequency  may  be  as  much  as 
one  and  one-half  times  as  great  as  for  the  straight  oscillator  of  the  same 
wire  length  and  the  wave  length  correspondingly  only  two-thirds  that  of 
the  straight  wire.  For  short,  wide  coils,  however,  the  frequency  is  always 
less*  (the  wave-length  always  greater)  than  for  a  straight  oscillator  of  the 
same  wire  length;  in  fact  the  coil  frequency  may  be  very  much  lower 
(the  wave-length  very  much  greater). 

Hence  the  frequency  of  the  fundamental  oscillation  f  of  a  coil  is 
not  directly  proportional  to  its  wire  length,  as  for  straight  oscillators, 
and  must  be  determined  experimentally,  unless  the  frequency  can  be 
determined  by  the  methods  already  described.28 

c.  A  characteristic  difference  between  relatively  long  thin  coils  and 
the   straight  lineal   oscillator  is  in   their  effective    capacity   [Art.   27], 
which  is  much  smaller  for  a  long  thin  coil  than  for  a  straight  wire  of  the 
same  length.     As  a  result,  with  such  coils  a  very  slight  change  in  the 
capacity  has  a  very  marked  effect  on  the  frequency.     A  small  piece  of 
metal,  in  fact  even  of  insulating  material,  brought  near  the  ends  of  the 
coil  is  sufficient  to  produce  a  noticeable  change  in  the  frequency  (''capacity- 
sensitiveness"  of  coils). 

d.  A  further  characteristic  difference  lies  in  the  extremely  low  radiation 
of  coils  as  compared  to  straight  lineal  oscillators.     Hence  radiation  plays 
but  a  very  slight  part  in  the  damping  of  coils,  so  that  as  long  as  there  is 
no  leakage  discharge  the  damping  of  coils  is  determined  almost  entirely 
by  the  Joulean  decrement.     For  coils  without  a  spark  gap,  whose  wires 
are  massive  but  neither  extremely  thick  nor  thin,  the  decrement  is  of 
about  the  same  order  of  magnitude  as  for  a  condenser  circuit  with  spark 
gap.     By  the  use  of  flat  copper  strip  or  of   braids  whose  strands   are 
individually  insulated  [Art.  36d]  and  by  proper  design  of  the  coils,  the 

*  If  the  coil  length  is  about  twice  its  diameter,  then  the  wave-length  is  approxi- 
mately the  same  as  for  the  straight  wire  oscillator,  i.e.,  it  is  twice  the  wire  length, 
f  And  also  of  the  upper  harmonics. 
3 


34  WIRELESS  TELEGRAPHY 

decrement  can  be  brought  just  as  low  as  for  condenser  circuits  without 
a  spark  gap.29 

No  systematic  investigations  have  as  yet  been  made  as  to  just  how 
the  decrement  of  coils  is  affected  by  leakage  discharge.  Such  observations 
as  have  been  made,  however,  indicate  that  the  effect  is  quite  marked.30 

2.  GENERAL  PROPERTIES  OF  OPEN  OSCILLATORS 

24.  Current  and  Potential  Distribution  Along  a  Wire. — Consider  a 
portion  of  an  oscillator  of  any  kind  and  any  frequency  to  consist  of  a 
straight  or  at  least  not  extremely  bent  (e.g.,  wound  in  coil  form)  wire. 
Then  the  following  holds  approximately  true  for  the  distribution  of 
current  and  potential  along  the  wire:30 

a.  The  curve  of  current  distribution  is  a  part  of  the  sine  curve  repre- 
senting the  current  distribution  of  a  straight  lineal  oscillator  of  the  same 
frequency  [Art.  18].  The  same  applies  to  the  potential  curve. 


That  is,  in  accordance  with  Art.  19,  the  current  and  potential  curves 
for  the  wire  are  parts  of  sine  curves,  whose  nodes  (or  anti-nodes)  have  a 
distance  apart  (which  is  a  half  wave-length)  as  given  by  the  relation 

X        VL 

2~2N 

in  which  N  is  the  frequency  of  the  oscillator. 

b.  Just  as  for  the  straight  lineal  oscillator  (Figs.  23,  33,  34,  35),  the 
current  anti-nodes  coincide  with  potential  nodes  and  vice  versa.  The 
relation  between  the  current  amplitude  |/0  at  the  current  anti-node  to 
that  of  the  potential  |F0  at  its  anti-node  depends  mainly  upon  the 
dimensions  of  the  wire.  We  have 

(2) 


|F0| 

in  which  C(1)  and  L(1)  indicate  the  capacity  and  coefficient  of  self-induc- 
tion respectively  of  the  length  of  wire  considered  as  a  unit. 

c.  Whether  any  nodes  and  anti-nodes  of  current  and  potential  exist 
at  all  on  the  wire,  and  if  so,  at  what  points,  depends  on  the  shape  of  the 
entire  oscillator  and  the  nature  of  its  oscillations.  If  one  end  of  the  wire 


OPEN  OSCILLATORS 


35 


is  free,  there  must  necessarily  be  a  current  node  (potential  anti-node) 
at  that  end,  as  the  current  must  be  constantly  zero  at  this  point. 

Thus  if  B  in  Fig.  36  is  the  free  end  of  a  wire  oscillator,  the  current  and 
potential  distribution  must  be  about  as  shown  in  the  figure.  Here  the 
portion  A  B  =  one-fourth  of  the  wave-length  according  to  equation  (1). 

If  the  oscillator  consists  of  two  symmetrical  halves,  the  fundamental 
oscillation  must  have  its  current  anti-node  (potential  node)  at  the  center 
of  the  oscillator.* 

25.  The  Electromagnetic  Field  at  Great  Distances  from  the  Oscillator. 
— a.  Consider  the  straight  wire  oscillator  AB,  shown  in  Fig.  37,  to  have 
a  length  I,  very  short  in  comparison  to  the  wave-length  of  the  oscilla- 
tion, f  so  that  the  current  amplitude  is  practically  the  same  at  all  points 
of  the  wire.  Then  the  relations  determining  the  electromagnetic  waves 
radiated  by  such  an  oscillator  become  very  simple,  if  we  limit  ourselves 
to  distances,  r,  from  the  wire  which  are  very  great  as  compared  to  the 
wave-length. 

A 


FIG.  37. 

It  should  be  noted  that  the  relations  which  follow  are  quite  different 
from  those  which  apply  to  static  fields.     We  have  then: 

1.  At  any  point,  P  (whose  distance  r  from  AB  is  much  greater  than 
the  wave-length)  the  direction  of  the  electric  field  lies  in  the  plane  con- 
taining P  and  the  wire  AB.     In  Fig.  37  this  is  the  plane  of  the  page. 
It  is  perpendicular  to  the  radius  r.     The  magnetic  flux  M  is  perpen- 
dicular to  the  plane  of  the  page  at  P. 

2.  The  respective  amplitudes  of  the  electric  and  magnetic  fields  are: 


M, 


r'X 


'   x 
2 

sin  &  = 


sn 


-  C.G.S. 

l 


sn  * 


C.G.S. 


*  For  example,  this  would  apply  to  a  condenser  circuit  as  shown  in  Fig.  1,  in  which 
the  current  node  occurs  at  F.  From  what  has  been  said  it  follows  that  the  statement 
[Art.  18a]  that  the  current  amplitude  is  the  same  at  all  points  of  a  condenser  circuit 

holds  true  only  as  long  as  the  length  of  the  circuit  is  very  small  as  compared  to  „.     To 

be  sure,  this  is  probably  always  the  case  for  condensers  as  used  in  practice. 

t  This  can  be  accomplished  by  placing  bodies  of  relatively  large  capacity  at  the 
ends  A  and  B  [Art.  28]. 


36  WIRELESS  TELEGRAPHY 

That  is,  the  field  strength  is  proportional  to  the  current  amplitude,  J0, 
the  frequency,  N,  of  the  oscillation  and  to  the  projection,  A'B',  of  the 
wire  length,  I,  on  a  line  perpendicular  to  r  (A'B'  =  I  sin  $  in  Fig.  37). 

3.  The  phase  of  the  electric  and  of  the  magnetic  fields  is  the  same.* 
The  difference  in  phase  with  the  current  depends  on  the  distance  r.33 
It  increases  as  for  all  advancing  waves  [Art.  206],  proportionally  to  r; 

if  r  is  increased  by  an  amount  x,  the  phase  difference  increases  by 

x 

Hence  the  oscillations  at  two  points  at  respective  distances  r\  and  r2 
may  be  considered  as  having  the  same  phase  only  if  r\  —  r2  is  very  small 
as  compared  to  X. 

6.  The  results  stated  above  may  be  used  for  calculating  the  electro- 
magnetic field  of  any  oscillator  at  any  point,  P,  whose  distance  from 
the  oscillator  is  great  compared  to  the  wave-length.34  The  correct  value 
of  the  field  can  be  obtained  by  applying  the  following  rule:  Consider 
the  oscillator  subdivided  into  small  elements  h,  Z2,  etc.,  sufficiently  short 
to  have  the  current  amplitudes  (Jlo,  72o,  etc.),  constant  throughout 
each  length.  Then  calculate  the  field  strength  for  each  element  from 
equation  (1),  given  in  a.  The  partial  fields  so  obtained  are  then  com- 
bined, giving  the  total  resultant  field,  f 


FIG.  38. 

c.  This  method  becomes  very  simple  if  the  oscillator  is  unidirectional 
(AB  in  Fig.  38)  and  if  the  field  is  to  be  calculated  for  a  very  distant 
point  in  or  very  close  to  the  equatorial  plane. 

We  then  have  the  angle  #  [a]  =  90°  for  all  the  current  elements,  so 
that  the  individual  partial  fields  have  the  same  direction.  Also  the 
distance  r  of  the  different  current  elements  is  practically  the  same  and 
hence  the  partial  fields  all  have  the  same  phase.  Hence,  under  these 
conditions  the  amplitude  of  the  resultant  field  equals  the  sum  of  the 
amplitudes  of  the  partial  fields,  i.e., 


M0  =  y  •  ~  (IJ^  +  Z2/2o 


(2) 


*  Assuming  that  E  and  M  are  considered  positive  in  the  directions  of  the  arrows 
in  Fig.  37. 

t  Allowance  must  be  made  not  only  for  the  difference  in  direction  of  the  partial 
fields,  but  also  for  their  phase  differences. 


OPEN  OSCILLATORS 


37 


The  factor  (Ui0  +  M 2o  +  .  .  . )  means  the  sum  of  the  products  of  the 
length  and  the  corresponding  current  amplitude  of  each  element. 

This  result  may  be  expressed  in  various  ways: 

1.  The  summation  factor  in  parentheses  is  nothing  other  than  the 
product  of  the  oscillator  length  and  the  average  value,  70,35  of  the  current 
amplitude  in  the  oscillator  equation  (2)  may  therefore  also  be  written: 

j  j 

—   =  2irN  ,  I  .  — 
T  r 

(3) 


2.  As  the  average  value  of  the  current  amplitude  along  the  entire 
length  of  the  oscillator  can  not  be  measured  directly,  it  is  more  con- 


FIG.  39. 

venient  to  introduce  the  maximum  current  amplitude  |/o|  at  the  anti- 
node.     For  the  given  current  distribution  70  is  proportional  to  |/0|,  i-e-, 

Io  =  a  |/o| 

The  factor  a,  which  is  determined  by  the  nature  of  the  current  dis- 
tribution, is  called  the  "form  factor"  of  the  oscillator. 

If  the  current  amplitude  is  the  same  at  all  points  along  the  oscillator 
[Art.  28]  a.  =  1,  which  of  course  is  its  maximum  value.  As  the  other 
extreme,  we  have  the  case  of  the  current  distribution  curve  on  each 
half  of  the  oscillator  being  practically  a  straight  line  passing  through  the 
end  of  the  oscillator  [Art.  3 la];  here  a  =  J^.36  If  the  current  distribu- 
tion curve  is  a  pure  sine  curve  as  in  Fig.  23,  then  a  =  2/7r.*'37 

*  This.,  value  of  a  substituted  in  equation  (4)  page  38  gives  the  equations  in  Art. 
20d,  remembering  that  I  =  X/2  [Art.  196]. 


38  WIRELESS  TELEGRAPHY 

Introducing  the  form  factor  into  equations  (3),  we  obtain: 

fL .  L°i  =  2-n-  ~ .  L^I  3  x 
X      r  X      r 

™7     II" J  Volts         «    „       ,     ^u,  .   . 

r         rcm         cm 

:  l/o 


"  X      r          3  X  1010        '   r 

3.  Interpreting  this  geometrically,  if  we  plot  the  curve  of  current 
distribution  by  plotting  the  current  values  as  ordinates  at  each  current 
element  and  connecting  the  points  thus  obtained  (dotted  curve  in  Fig. 
39*),  then  the  area  (shaded  in  Fig.  39)  included  by  this  curve  and  the 
oscillator  =  (Zi/i0  +  Wao  + )•  Hence  it  follows  from  equa- 
tion (2)  that  the  area  included  by  this  curve  is  a  measure  of  the  amplitude 
of  the  electromagnetic  field  in  distant  parts  of  the  equatorial  plane.  That  is, 
the  current  distribution  curve  is  also  characteristic  of  the  effect  at  remote 
distances. 


FIG.  41. 

d.  This  construction  can  easily  be  applied  to  more  complicated  oscil- 
lators (e.g.,  of  the  form  shown  in  Fig.  40 f)  in  which  the  individual 
current  elements  have  different  directions.  A  straight  line,  AB,  is  drawn 
through  the  middle  point,  O,  of  the  oscillator,  perpendicular  to  the 
equatorial  plane.  At  each  point,  P,  of  this  line  ordinates,  PQ,  are 
erected  equal  to  the  sum  of  the  current  amplitudes  of  all  the  points 
(current  elements)  of  the  oscillator  which  lie  in  the  plane  containing 
P  and  parallel  to  the  equatorial  plane.  Thus  at  P  in  Fig.  40  we  have 
PQ  =  PiQi  +  P2Q2. 

The  area  (shaded  in  Fig.  40)  between  the  curves  (dotted  in  Fig.  40) 
thus  obtained  and  the  straight  line  AB  is  proportional  to  the  amplitude 
of  the  electromagnetic  field  at  very  distant  points  in  the  equatorial 
plane,  t 

*  The  curve  of  Fig.  39  has  been  purposely  chosen  of  arbitrary  form ;  it  would  be 
a  sine  curve  for  a  straight  lineal  oscillator. 

t  Oscillator  consisting  of  simple  straight  wire  at  the  center  with  two  branched 
wires  at  each  end. 

J  However,  this  construction  is  justified  only  if  the  width  of  the  oscillator  is  very 
small  as  compared  to  the  wave-length.  In  that  case  the  justification  of  this  con- 
struction follows  from  b  and  c. 


OPEN  OSCILLATORS  39 

e.  If  the  procedure  given  in  b  is  applied  to  a  closed  oscillator,  e.g., 
to  the  simplest  form  of  condenser  circuit  (Fig.  41),  whose  dimensions  are 
very  small  as  compared  to  the  wave-length  of  the  oscillation,  it  is  found 
that  this  oscillator  does  not  give  a  powerful  field  at  distant  points  as, 
say,  at  P.  The  partial  fields  of  the  individual  current  elements  (e.g., 
those  of  ab  and  cd,  Fig.  41)  practically  neutralise  each  other. 

Much  the  same  is  true  of  coils. 

26.  The  Radiation  of  an  Oscillator. — In  Art.  25  it  was  shown  how  to 
determine  the  amplitude  of  the  electric  and  magnetic  field  at  distant 
points  in  the  equatorial  plane  of  any  oscillator.  The  amplitude  of  this 
electromagnetic  field  is  to  a  certain  extent  a  measure  of  the  energy 
radiated  by  the  oscillator. 

a.  Imagine  a  sphere  whose  center  is  that  of  the  oscillator  and  whose 
radius  is  very  large  compared  to  the  wave-length;  then  the  amount  of 
energy  passing  through  1  sq.  cm.  of  the  surface  of  the  sphere  during  each 
cycle  or  period  is 


EQ  and  MQ  representing  the  amplitude  of  the  electric  and  magnetic  fields 
respectively  at  the  point  in  question.370 

If  the  amplitude  at  all  points  were  as  great  as  in  the  equatorial  plane, 
then  the  quantity  of  energy  passing  through  the  total  surface  F  of  the 
sphere,  per  cycle,  which  is  also  the  total  radiation  per  cycle,  would  be 

T  .F 

in  which  \EG\  and  \M0\  represent  the  field  amplitude  in  the  equatorial 
plane.  As  a  matter  of  fact,  however,  the  field  strength  decreases  from 
the  equator  to  the  poles,  and  the  actual  total  radiation  per  cycle  is 


the  factor  7  being  less  than  unity  and  depending  upon  the  nature  of  the 
decrease  of  the  field  strength  from  the  equator  to  the  poles.  While  this 
factor  varies  with  different  types  of  oscillators,  the  variation  is  so  small 
as  to  be  negligible  for  qualitative  considerations.*  From  the  foregoing, 
we  may  therefore  conclude:  The  greater  the  amplitude  of  the  electric  and 
magnetic  fields  at  distant  points  in  the  equatorial  plane,  the  greater  is  the 
radiation  of  the  oscillator,  f 

6.  According  to  Art.  25  both  EQ  and  MQ  are  proportional  to    |/0 

*  For  sinusoidal  current  distribution  7  =  0.61,  while  for  even  distribution,  i.e., 
the  same  current  amplitude  at  all  points  along  the  oscillator,  7  =  0.67. 38 

t  The  amplitude  of  the  electromagnetic  field  in  the  vicinity  of  the  oscillator  is 
absolutely  no  indication  of  the  amount  of  radiation. 


40  WIRELESS  TELEGRAPHY 

Hence  the  energy  radiated  per  cycle  varies  as  |/o|2  X  T  and  the  energy 
radiated  per  second,  that  is,  the  radiation,  S  [see  Art.  21o],  is  proportional 
to  |/|2e//,  if  \I  2ef/  is  the  average  time  value  of  |/|2.  Hence  we  may 
write  the  energy  radiated  per  second 

s  =  flz.|/|V/  (i) 

The  expression  for  the  energy  lost  by  radiation  thus  arrived  at  is  entirely 
analogous  to  that  for  the  energy  lost  as  heat  developed  by  the  resistance 
of  the  circuit  (  =  jft|/|2e//[Art.  27  a]).  In  view  of  this  analogy  R  2  is  called 
the  "radiation  resistance"  of  the  oscillator. 

From  this  definition  and  from  the  relations  explained  in  Art.  25, 
it  follows  that  R-^^l^^N2  or  1/X2.  Approximately  (R.  RtJDENBERG39) 
we  have: 


=  807T2  (—}  2  ohms  [see  Table  XIII]  (2) 

At  one  limit  (same  current  amplitude  throughout  the  entire  oscil- 
lator) a  =  1  [Art.  25c],  and 

RX  =  807r2(,  )  ohms  =  approx.  800  Lj  ohms 

while  for  the  other  limiting  case  a  =  0.5  and 

/l\2  /l\2 

RZ  =  207r2(-j  ohms  =  approx.  200  (-1  ohms. 

For  the  case  of  sinusoidal  current  distribution  of  the  form  shown  in 
Fig.  23  (a  =  2/7T,  I  =  X/2)  equation  (2)  gives  R?  =  80  ohms.  Actually, 
however,  as  shown  by  a  more  accurate  calculation26  the  radiation 
resistance  in  this  case  is 

R?  =  73.2  ohms. 

27.  Effective  Capacity  and  Effective  Self-induction  of  an  Oscillator.— 

a.  It  is  frequently  convenient  to  express  the  frequency,  N,  the  wave- 
length, X,  and  the  Joulean  decrement,  dj,  of  an  oscillator  similarly  to  the 
expressions  for  a  condenser  circuit,  viz., 


*  Or  [Art.  Sd]. 

,  «nn    2fl»**"  CMF  2      R* 

d}-  =  600*-8— r—        -  =  approx.       ^  1 

hmeteis  OUU        / 


OPEN  OSCILLATORS  41 

The  quantities  designated  herein  by  R,  L  and  C  are  called  the  "effective 
resistance,"  "effective  coefficient  of  self-induction"  and  "effective 
capacity"  respectively. 

R  may  be  defined  as  being  that  value  in  the  expression  R\I\2eff  when 
this  is  equal  to  the  energy  dissipated  as  (Joulean)  heat  per  second,40 
if  |/|  is  the  current  at  that  point  of  the  oscillator  at  which  the  maximum 
current  amplitude  occurs.*  L  and  C  are  then  defined  by  equations  (1) 
and  (2). 

From  this  definition  of  R  it  follows  that  R — the  same  being  true  also 
of  L  and  C — depends  not  only  on  the  dimensions  of  the  oscillator,  but 
also  on  the  frequency  and  on  the  resulting  distribution  of  current  and 
potential.  For  example,  these  quantities  will  have  different  values  for 
the  fundamental  and  for  the  upper  harmonic  oscillations. 

If  Fo|  is  the  maximum  potential  amplitude  occurring  at  any  point 
of  the  oscillator,  and  if  |/o|  is  the  maximum  current  amplitude,  then  we 
have 


in  which  /3  is  a  factor  whose  value  for  the  majority  of  cases  encountered 
in  practice  differs  only  slightly  from  1. 

b.  Just  as  the  Joulean  decrement  is  determined  by  the  ohmic  re- 
sistance, so  the  radiation  decrement  d%  may  be  expressed  in  terms  of 
the  radiation  resistance: 


3.  VARIOUS  FORMS  OF  COMPLEX  OSCILLATORS 

28.  Lineal  Oscillator  with  Two  Equal  Capacities,  One  at  Each  End 
(Hertz  Oscillator).  —  a.  The  effective  capacity  of  the  oscillator  is  in- 
creased by  the  conductors  {  attached  at  the  ends.  Hence  the  frequency 
will  be  lower  and  the  wave-length  greater  than  for  a  simple  wire  of  the 
same  length.  The  difference  is  the  greater  as  the  end  capacities  are 
greater  in  proportion  to  effective  wire  capacity. 

b.  The  distribution  of  current  and  potential  must  be  as  shown  in 
Fig.  42.  §  The  greater  the  attached  end  capacities  are  as  compared  to 

*  Generally  this  is  the  current  value  at  the  anti-node. 
t  Or  [Art.  Sd] 

.RZohmsCMF  2 

-  —        - 


_nn     .o 

d?  =  6007T2  -  —        -  =  approx.  ^ 

^meters  OUU          ^meters 

$  It  is  assumed  that  the  conductors  mentioned  here  and  in  what  follows  have 
dimensions  so  small  in  comparison  to  the  wave-length  that  the  potential  may  be 
considered  as  the  same  at  all  parts  of  the  conductor.  This  is  largely,  though  not 
entirely  true  of  spheres,  circular  or  rectangular  sheets  of  metal  or  wire  meshes. 

§  In  regard  to  shaded  portion  of  this  and  following  figures,  see  Art.  33. 


42 


WIRELESS  TELEGRAPHY 


the  effective  wire  capacity,  the  nearer  does  the  minimum  current  ampli- 
tude at  any  point  of  the  wire  approach  the  current 
amplitude  at  the  anti-node,  i.e.,  the  curve  of  cur- 
rent distribution  approaches  a  straight  line  paral- 
lel to  the  oscillator,  and  the  form  factor  approaches 
1.0  in  value. 

The  current  amplitude  at  its  anti-node  is  deter- 
mined by  the  potential  amplitude  at  its  anti-node 
from  equation  (2)  Art.  24.  As  a  matter  of  fact  the 
highest  potential  on  the  oscillator  occurs  at  the 
end  capacities.  Hence  the  current  amplitude  is 
much  greater  in  relation  to  the  maximum  potential 
amplitude  than  it  would  be  for  a  simple  wire  of 
the  same  length. 

c.  If  we  compare  such  an  oscillator,  as  regards 
effectiveness  at  a  distance,  with  a  lineal  oscillator 
of  the  same  length,  the  former  (HERTZ  transmitter) 
has  the  advantage  of  its  high  current  value  at  the 
current  anti-node  and  the  high  value  of  its  form 
factor  [Art.  25c].  On  the  other  hand,  from  equa- 
tion (2)  Art.  25  the  longer  wave-length  of  the 
HERTZ  oscillator  would  be  unfavorable.  How- 
ever,41 in  spite  of  this  latter  condition,  the  effec- 
tiveness at  a  distance  of  a  HERTZ 
oscillator  is  greater  than  that  of  a 

lineal  oscillator  of  the  same  wire  length,  assuming  that 
the  maximum  potential  amplitude  is  the  same  on  both 
oscillators. 

29.  Lineal  Oscillator  with  Capacity  at  One  End. — 
a.  Current  and  potential  distribution  are  shown  in  Figs. 
43  and  44,  for  a  moderate  capacity  in  Fig.  43,  for  a  very 
large*  capacity  in  Fig.  44.  The  larger*  the  capacity 
attached  at  one  end  is,  the  greater  is  the  wave-length 
of  the  oscillation  and  the  farther  from  the  middle  of 
the  wire  does  the  current  anti-node  (and  node  of  poten- 
tial) occur,  coming  nearer  to  the  end  capacity. 

If  the  attached  end  capacity  is  extremely  great  as 
compared  to  the  effective  capacity  of  the  wire,  then 
the  current  anti-node  (also  the  node  of  potential)  is  but 
very  slightly  displaced  from  the  end  capacity;  hence  the 
wire  length  is  about  equal  to  one-quarter  of  the  wave- 
length (Fig.  44). 

6.  The  following  will  explain  why  the  potential  node  and  current 
*  In  comparison  to  the  effective  wire  capacity. 


FIG.  42. 


43. 


OPEN  OSCILLATORS 


43 


anti-node  must  necessarily  occur  at  the  capacity  in  the  last-mentioned 
case.  The  relation  between  potential,  F0,  and  current,  70,  amplitudes 
at  any  point  is  given  by 

/„  =  eo  CF0 

Hence  if  the  capacity,  C,  of  the  attached  conductor  is  very  large,  F0 
must  be  very  small  for  a  given  value  of  70.*  It  follows  that,  if  a  con- 
ductor of  very  great  capacity  is  attached  to  an  oscillator  at  any  point,  a 
node  of  potential  and  a  current  anti-node  will  occur  at  or  very  near  to 
this  point.  If  a  potential  node  (current  anti-node)  already  existed  at 
this  point,  the  addition  of  capacity  will  not  change 
the  distribution  of  current  and  potential  from  the  pre- 
vious condition. 

c.  The  conditions  indicated  in  Figs.  43  and  44 
may  also  be  conceived  in  a  somewhat  different  way. 
Given  the  portion  OA  in  Fig.  43  and  the  current 
and  potential  distribution  along  OA.  This  distri- 
bution can  be  obtained  by  the  addition  of  a  sym- 
metrical portion,  OB,  forming  a  straight  lineal  oscil- 
lator. However,  the  portion  OB  can  be  replaced 
by  a  shorter  portion,  OC,  and  a  capacity  C,  so  chosen 
that  the  current  and  potential  distribution  on  OA  as 
well  as  the  frequency  remain  just  the  same  as  for 
the  symmetrical  oscillator  AOB.  The  shorter  OC 
is  in  relation  to  OA,  the  greater  must  be  the 
capacity  (7. 

30.  Lineal  Oscillator  Containing  Series  Condensers.42 — a.  Assume 
two  condensers  of  the  same  size  inserted  one  at  each  side  of,  and  at  a  dis- 
tance a  from  the  middle  point  of  a  lineal  oscillator.  We  may  then,  with 
sufficient  accuracy,  conceive  the  condenser  capacities  and  the  effective 
capacity  of  the  wire  as  being  simply  connected  in  series.  As  a  matter 
of  fact  the  introduction  of  the  condensers  does  reduce  the  effective  ca- 
pacity of  the  oscillator.  The  result  is  an  increase  in  frequency  and 
thereby  a  shortening  of  the  wave  length,  which  is  the  more  marked  the 
smaller  the  introduced  capacity  is  in  proportion  to  the  effective  capacity 
of  the  wire. 

The  distribution  of  current  and  potential  must  be  approximately  as 
shown  in  Fig.  45.  This  follows  partly  from  the  effect  of  the  frequency 
upon  current  and  potential  distribution  discussed  in  Art.  24,  partly  from 
the  relation  between  the  current  amplitude  /o  at  the  condenser  of  capacity 
C  and  that  of  the  potential,  Vi  —  V2,  between  the  condenser  coverings, 
viz., 

70  = 


O 


FIG.  44. 


*  w  ( =  2-n-N)  does  not  become  very  small  at  the  same  time. 


44 


WIRELESS  TELEGRAPHY 


b.  If  the  two  condensers  are  brought  nearer  together  at  the  center  of 
the  oscillator  until  they  may  be  replaced  by  a  single  condenser,  the 
current  and  potential  distribution  will  be  as  shown  in  Fig.  46. 

c.  If  the  inserted  condenser  or  condensers  have  very  great  capacity,  as 
compared  to  the  effective  capacity  of  the  wire,  their  introduction  has  no 
appreciable    effect    upon   the    characteristics    of   the    oscillation,    inde- 
pendently of  the  point  at  which  the  condensers  are  added. 


FIG.  46. 

31.  Lineal  Oscillator  Containing  Series  Inductance. 42 — a.  The  intro- 
duction of  coils  increases  the  effective  coefficient  of  self -induction  of  the 
oscillator.  The  result  is  reduced  frequency  with  increased  wave-length. 
The  extent  of  the  change  depends  upon  the  dimensions  of  the  coil  as 
compared  to  those  of  the  rest  of  the  oscillator.  For  a  given  oscillator 
the  coefficient  of  self-induction  of  the  coil  is  a  good  measure  for  the 
change  in  wave-length:*  the  greater  the  coefficient  of  self-induction  of  the 
coil  is,  the  greater  will  be  the  change  in  wave-length  caused  by  its 
introduction. 

The  distribution  of  potential  and  current  must  be  as  shown  in  Fig.  47, 
assuming  that  the  length  AC  =  Y±  wave-length.  Only  that  portion  of 
the  current  curve  which  is  near  the  current  node  lies  on  the  wire.  Hence 
the  average  current  amplitude  is  comparatively  low  and  also  the  maxi- 
mum current  amplitude  occurring  on  the  oscillator  is  much  less  than  it 
would  be  for  a  straight  lineal  oscillator  corresponding  to  the  same  poten- 
tial amplitude. 

*  At  least  for  such  cases  as  are  encountered  in  practice. 


OPEN  OSCILLATORS 


45 


FIG.  47. 


The  greater  the  self-induction  of  the  inserted  coil,  the  greater  will  be 
the  wave-length  of   the  oscillations  as  compared  to  the  length  of  the 
oscillator  and  the  more  will  the  curve  of  current  dis- 
tribution on  each  half  of  the  oscillator  approach  a 
straight  line  passing  through  the  end  of  the  oscillator, 
the  form  factor  a  approaching  J<j  in  value. 

b.  The  coil  adds  nothing  appreciable  to  the  distance 
effect  [Art.  25e];  the  current  distribution  along  the 
straight  part  of  the  oscillator,  with  its  low  form  factor 
is  very  unfavorable  for  distance  effect,  while  the  in- 
crease in  wave-length  due  to  the  coil  has  the  same  un- 
favorable tendency.  All  these  factors  tend  jointly  to 
considerably  reduce  the  distance  effect,  as  well  as  the 
radiation  resistance  of  such  an  oscillator,  as  against  a 
straight  lineal  oscillator  of  the  same  length  and 
potential. 

Moreover,  as  the  effective  capacity  of  an  oscillator 
of  the  form  shown  in  Fig.  47  is  practically  the  same 
as  that  of  a  lineal  oscillator  of  the  same  length,  while 
the  effective  coefficient  of  self-induction  is  much 
greater,  it  follows,  from  equation  (3)  Art.  27,  that  the  radiation  decre- 
ment is  much  smaller  for  an  oscillator  containing  a  series  coil  than  for  a 
straight  oscillator  of  the  same  length. 

32.  Lineal  Oscillator  with  Both  Inductance  and  Ca- 
pacity.— a.  The  decrease  in  frequency  caused  by  the  in- 
troduction of  coils  can  be  either  entirely  or  partly  com- 
pensated for  by  the  introduction  of  condensers,  or  con- 
verted into  an  increase  in  frequency  [Art.  30].  Just 
which  of  these  three  possibilities  will  result  depends  upon 
the  relative  values  of  the  self-induction  and  the  capacity, 
other  things  being  equal.  If  the  coils  have  the  greater 
effect,  the  distribution  of  current  and  potential  will  be 
similar  to  that  shown  in  Fig.  47,  while  if  the  condenser 
effect  is  the  greater,  the  distribution  will  be  as  shown  in 
Fig.  45  or  46. 

If  the  effect  upon  the  frequency  of  the  coils  is  exactly 
compensated  for  by  that  of  the  condensers,  then  the  cur- 
rent and  potential  distribution  along  the  straight  portion 
of  the  oscillator  (Fig.  48)  is  about  the  same  as  for  an 
ordinary  straight  oscillator  of  the  same  length. 

b.  In  one  respect,  however,  the  oscillator  of  Fig.  48* 
differs  very  materially  from  a  simple  straight  oscillator 
of  the  same  length,  viz.,  the  radiation  decrement  of  the  former  is  much 
*  The  reader  must  imagine  a  symmetrical  lower  half  for  Fig.  48. 


FIG.  48. 


46  WIRELESS  TELEGRAPHY 

less  than  for  the  latter  as  obtained  from  the  relations  given  in  Art.  26 
and  276.  Hence  oscillators  of  the  form  shown  in  Fig.  48  are  frequently 
referred  to  as  "oscillators  with  reduced  radiation  damping." 

33.  Grounded  Oscillators. — It  was  shown  in  Art.  29  that  one-half  a 
straight  lineal  oscillator  may  be  replaced  by  a  capacity  connected*  at 
the  center  (current  anti-node)  without  noticeably  changing  the  distribu- 
tion of  current  and  potential  for  the  fundamental  oscillation  of  the 
remaining  half  of  the  oscillator.  This  is  by  no  means  restricted  to  the 
plain  lineal  transmitter,  but  holds  equally  good  for  any  of  the  classes  of 
oscillator  discussed  in  the  preceding  paragraphs. 

The  earth  may,  within  certain  limits,  be  considered  as  such  a  large 
capacity  on  condition  that  it  is  highly  conductive  at  the  point  in  question. 
If  then,  in  the  oscillators  previously  described,  we  assume  a  half  of  each 
removed  and  the  remaining  half  directly  connected  to  a  conductive  por- 
tion of  the  earth,  i.e.,  "grounded,"  the  current  and  potential  distribu- 
tion in  each  case  will  remain  unchanged.  The  distribution  curves  of 
Figs.  42  to  48  therefore  are  also  correct  if  only  the  upper  half  of  each 
oscillator  remains  and  the  lower  half,  shown  in  the  shaded  area,  is  re- 
placed by  a  "good  ground."  Moreover,  what  has  been  stated  in  the 
preceding  in  regard  to  the  frequency  and  wave-length  of  the  fundamental 
oscillation  of  symmetrical  oscillators  holds  equally  true  for  the 
grounded  half. 

*  i.e.,  directly  connected  by  actual  contact,  not  by  any  means  through  a  wire  con- 
nection of  any  material  length. 


CHAPTER  III 

THE  HIGH  FREQUENCY  ALTERNATING -CURRENT  CIRCUIT 
1.  RESISTANCE,   SELF-INDUCTION  AND  CAPACITY 

34.  Current   Distribution   in   Cross-section   of    Solid   Wires. — For 

direct  currents  and  also  approximately  for  alternating  currents  of  such 
frequencies  as  are  used  for  commercial  power  and  lighting  purposes,  the 
current  per  unit  area  is  the  same  at  all  parts  of  the  cross-section  of  the 
conductor.  But  with  the  high  frequencies  customarily  employed  in 
wireless  telegraphy,  the  current  density  is  always  greatest  in  the  parts 
nearest  the  surface  of  the  wire.  It  decreases  as  the  center  of  the  wire  is 
approached,  the  decrease  being  most  rapid  for  higher  frequency,  higher 
conductivity  and  higher  permeability  of  the  material  of  the  wire.  This 


>•  Distance  below  Surface  of  Wire  in  mm 

FIG.  49. 

decrease  may  be  so  rapid  that  practically  the  entire  current  is  restricted 
to  a  very  thin  outer  sheath  of  the  wire  (the  so-called  "skin  effect"). 

Fig.  49*  shows  the  drop  in  current  density  in  copper  wire  as  the 
depth  from  the  surface  is  increased,  for  various  frequencies. 

35.  Coefficient  of  Self -induction.44 — If  the  skin  effect  is  very  decided, 
there  is  practically  no  magnetic  field  within  the  wire.  While  for  direct 
currents  the  coefficient  of  self-induction  of  the  circuit  is  made  up  of  two 
parts,  one  originating  from  the  field  inside  of  the  wire,  the  other  from  the 

*  The  minimum  wire  radius  for  which  the  curves  of  Fig.  49  still  hold  good,  at 
N  =  0.5  X  106/sec.,  is  about  3  mm.;  at  N  =  2.5  X  105/sec.,  about  1.6  mm.;  and  at 
N  =  5.0  X  105/sec.,  about  1.1  mm.  With  thinner  wires,  the  drop  in  current  density 
is  not  so  rapid. 

47 


48  WIRELESS  TELEGRAPHY 

field  without  the  wire,  for  high  frequency  alternating  currents  the  first 
part  (which  for  non-ferromagnetic  straight  wires  of  length  I  cm.  amounts 

to  ~  C.G.S.  units)  practically  disappears.     No  great  error  will  be  made  if 

Z 

for  straight  or  nearly  straight  solid  wires  the  first  part  is  neglected  and 
the  "effective  coefficient  of  self-induction,"  L,  for  high  frequencies  is 

calculated  by  deducting  ~  C.G.S.  units  from  the  value  applying  to  direct 

currents  (see  Table  VI) .  For  wires  which  are  much  bent,  however,  the 
relations  are  not  so  simple*  (see  Art.  37). 

If  the  development  of  a  skin  effect  is  prevented  by  the  use  of  properly 
woven  and  twisted  braid,  consisting  of  individually  insulated  wires 
[Art.  36d],  the  effective  coefficient  of  self-induction,  L,  for  oscillating 
currents  will  not  differ  materially  from  that,  Ls,  for  direct  current,  this 
being  true  not  only  of  straight  wire  circuits,  but  also  of  coils  wound  in  a 
single  layer.45 

36.  Resistance  of  Straight  Wires. — A  further  result  of  the  uneven 
distribution  of  the  current  is  that  the  cross-section  of  the  thin  outer 
sheath,  in  which  the  flow  of  current  is  concentrated,  rather  than  the 
section  of  the  entire  wire,  determines  its  resistance  to  high  fre- 
quency currents.  In  fact  the  so-called  "effective"  resistance,  R,  of  a 
wire  also  called  the  alternating-current  resistance  for  high  frequency 
oscillations  [Art.  8a],  is  something  quite  different  from  the  resistance  for 
direct  current.  This  difference  increases  as  the  frequency,  the  radius  of 
the  wire,  its  conductivity  and  its  permeability  become  greater.46 

a.  Table  VII  at  the  end  of  the  book  gives  the  resistance  of  copper 
wires  of  various  sizes  and  for  different  frequencies  encountered  in  radio 
practice.     The  resistance  of  iron  wire  is  much  higher  on  account  of  high 
permeability  so  that  for  this  reason  alone  its  use  in  practice  is  forbidden. 

b.  For  very  thin  wires,  particularly  when  made  of  metal  having  low 
conductivity,  the  effective  resistance  at  radio  frequencies  is  but  little 
different  from  that  for  direct  current,  the  difference  decreasing  as  the 
size  of  wire  decreases.     In  Table  VIII  are  given  those  sizes  of  wire  of 
different  material  and  at  different  frequencies  for  which  this  variation 
from  the  direct-current  resistance  is  just  1  per  cent. 

Resistances47  which  are  practically  non-inductive  and  practically 
independent  of  the  frequency  can  be  made  up  of  thin  wires  of  constantan, 
manganin  and  nickelin  for  small  currents,  while  braids  of  these  wires 
individually  insulated,  arc  lamp  carbons,  graphite  rods  and  also  glass 
tubes  containing  an  electrolyte,  such  as  CuSO4  solution,  serve  for  larger 
currents. 

*  The  coefficient  of  self-induction  of  coils  made  of  heavy  wire  may  be  about  20 
per  cent,  less  for  high  frequency  oscillations  than  for  direct  current.45  Formulae  for 
the  coefficient  of  self-induction,  L,  of  coils  are  given  in  Table  VI. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       49 

c.  The   following   conditions   are   closely   associated   with   the   skin 
effect  : 

1.  A  copper  tube  with  walls  not  extremely  thin  has,  to  all  intents  and 
purposes,  the  same  resistance  as  a  solid  wire  of  the  same  diameter  and 
material  (i.e.,  of  course,  for  high  frequency  currents). 

2.  Tinned  copper  wire  is  not  desirable,  as  the  current  is  carried  mostly 
by  the  poorly  conducting  tin,  making  the  resistance  higher  than  for  the 
untinned  wire. 

3.  Copper-clad  steel  wires  have  a  resistance  only  very  little  higher 
than  copper  wires,  and  combine  the  high  conductivity  of  the  copper 
with  the  greater  tensile  strength  of  the  steel,  which  is  very  advantageous 
for  antennae  submitted  to  high  wind  stresses.* 

d.  An  important  difference  between  the  resistance  for  direct  currents 
and  that  for  high  frequency  currents  lies  in  the  relation  to  the  wire  radius, 

r,  for  in  the  first  case  the  resistance  °c  — 2J  while  in  the  latter  case  (for 

wires  not  too  thin)  it  oc  -. 
.     r 

In  other  words  the  direct-current  resistance  simply  depends  on  the 
total  cross-section  of  the  conductor,  whether  this  is  a  single  wire  or  made 
up  of  a  number  of  wires  in  parallel  giving  the  same  total  cross-section. 

For  oscillating  currents  it  is  preferable  to  replace  heavy  solid  wires  or 
tubes  by  braids  of  very  thin  individually  insulated  wires  or  flat  bands  made 
up  of  such  braids  woven  together,  f  But  care  must  be  taken  that  the 
current  does  not  distribute  itself  much  the  same  as  it  would  in  a  solid 
wire,  i.e.,  mainly  in  those  of  the  smaller  wires  lying  near  the  outer  sur- 
face. This  is  provided  for  by  so  twisting  and  interweaving  the  component 
wires  that  each  of  them  lies  at  the  outside  just  as  many  times  as  on  the 
inside  of  the  circuit,  resulting  in  a  uniform  current  amplitude  in  all 
the  wires. 

Furthermore,  while  for  direct  currents  the  resistance,  aside  from  the 
specific  conductivity  of  the  material,  depends  only  on  the  area  of  the 
cross-section,  the  form  of  the  section  also  plays  a  part  in  determining  the 
effective  resistance  of  a  conductor  carrying  high  frequency  oscillations, 
e.g.,  thin  copper  bands49  in  general  have  a  lower  resistance  than  cylindrical 
copper  wire  of  the  same  cross-sectional  area,  though  the  resistance  of  the 
bands  also  increases  rapidly  with  increasing  frequency  unless  they  are 
exceedingly  thin. 

*  For  example,  the  antenna  of  the  Eiffel  Tower  has  galvanized  steel  wires. 

f  The  first  suggestion  to  use  woven  ropes  of  thin  insulated  wires  for  high  frequency 
circuits  probably  originated  with  N.  TESLA.SO  F.  DOLEZALEK  was  the  first  to  intro- 
duce them  into  actual  practice.  Braided  wire  of  this  kind  is  furnished  by  many 
manufacturers,  but  by  no  means  always  of  equal  value.  Braids  of  enameled  wire  (i.e., 
wire  having  very  thin  enamel  insulation)  of  0.07  mm.  diam.  are  very  satisfactory. 
4 


50 


WIRELESS  TELEGRAPHY 


37.  The  Resistance  of  Coils.45 — The  only  conductors  having  appre- 
ciable self-induction  encountered  in  radio  circuits  are  usually  in  the 
form  of  either  "cylindrical  coils"  (Figs.  50  and  51)  or  "flat  spirals" 
(Figs.  52,  53  and  54;  see  also  the  much  used  form  in 
Fig.  236  marked  "28"). 

a.  If  these  coils  are  made  of  solid  wire  the  current 
distribution  over  the  cross-section  is  subjected  to  a  fur- 
ther complication  as  compared  to  the  simple  straight 
solid  wire.  The  current  amplitude  is  no  longer  dis- 
tributed symmetrically  to  the  wire's  axis  but  is  consid- 
erably greater  on  the  inner 

side  of  the  coil  than  on  the      m  m 

outer  side.     This  results  in 
a  further  increase  of  the  re- 
sistance, so  that  the  effec- 
tive resistance   of  coils   as 
used  in  radio   work  is  apt  to  run  as  high  as  one  and  one-half  to  two 
times  that  of  the  same  wire  when  unbent. 

The  dissipation  of  energy  and  hence  the  effective  resistance  of  coils 
is  considerably  increased  if  they  are  so  constructed  that  a  large  proper- 


FIG.  50. 


FIG.  51. 


FIG.  52. 


FIG.  53. 


tion  of  the  magnetic  force  cuts  the  turns  of  the  wire  (as  for  example  at  the 
ends  of  the  coil). 

In  this  case,  however,  the  effective  resistance  may  often  be  reduced 
by  the  use  of  a  wide  copper  strip  or  band  in  place  of  wire  having  a 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       51 


circular  section,  or  better  yet,  conductors  made  up  of  small,  individually 
insulated  twisted  wires  (or  braids  or  bands  woven  out  of  such  conductors), 
the  thinness  of  the  individual  wires,  the  method  of  twisting  and  inter- 
weaving them  and  the  form  of  the  coil  determining  the  resultant  effective 
resistance. 

6.  With  coils  wound  in  several  layers  a  further  loss  due  to  dielectric 


FIG.  54. 

hysteresis  may  be  added.  With  alternating  current  a  relatively  high 
difference  of  potential  exists  between  adjacent  layers,  causing  a  cor- 
respondingly intense  alternating  electric  field  which  may  result  in  energy 
losses  in  the  insulating  material  affected.  For  this  reason  and  also  be- 
cause they  otherwise  tend  to  increase  the  energy  losses,  coils  wound  in 
several  layers  are  not  generally  desirable. 

38.  Coils  having  Variable  Self-induc- 
tion.52— a.  Changes  of  the  self-induction 
in  large  steps  are  most  easily  attained  by 
varying  the  number  of  turns  connected  in 
circuit,  say  through  the  use  of  plug  or  clip 
contacts;  thus  in  Fig.  55  the  current  enters 
through  A  and  leaves  the  coil  either  at  B  or 
CorZ). 

If  the  plug  contact  is  at  B,  then  the 
portion  BD  together  with  parts  of  the  cur- 
rent circuit  may  constitute  an  oscillator  which  is  directly  coupled 
[Art.  526]  with  the  current  circuit;  the  oscillations  of  this  system  may  at 
times  produce  undesirable  disturbances.  Furthermore,  losses  may  re- 
sult from  eddy  currents  induced  in  the  free  portion  (BD)  through  which 
flows  the  magnetic  flux  generated  in  the  connected  portion  (AB).  It  is 


52 


WIRELESS  TELEGRAPHY 


therefore  advisable  to  so  choose  coils  that  the  free  end,  BD,  does  not 
become  too  long. 

Under  no  circumstances  should  the  variation  of  the  self-induction  be 
obtained  by  short-circuiting  a  number  of  the 
turns    (e.g.,    BC,   Fig.   56).     Heavy  currents 
would  be  induced  in  the  short-circuited  por- 
tion, causing  a  large  energy  loss. 

6.  Self-induction  variations  in  small  steps 
may  be  obtained  by  the  use  of  sliding  con- 

/**• 


£ 


FIG.  57. 


FIG.  58. 


tacts.  Fig.  57  shows  this  method  as  applied  to  a  cylindrical  coil  and  Fig. 
58  to  a  modification  of  this,  the  "ring  coil."  The  latter  has  the  advan- 
tage of  enclosing  practically  all  its  lines  of  magnetic  force,  thereby 
minimizing  eddy  current  losses  in  neighboring  conductors  and  disturb- 
ances in  near-by  circuits.  The 
ring  coil,  however,  involves  greater 
construction  difficulties. 

Care  must  be  taken  with  coils 
of  the  form  of  Figs.  57  and  58  that 
the  sliding  contact  provides  good 
conductivity  and  that  it  does  not 
touch  more  than  one  wire  at  the 
same  time,  thereby  short-circuiting 
the  turn  included  between  them. 

c.  A  uniformly  gradual  change 
of  the  self-induction  is  attainable  in 
a  particularly  simple  manner  with 
flat  coils  (Fig.  59)  which  are  pro- 
vided with  a  rotating  arm,  K,  and 
a  movable  sliding  contact,  SC,  for 
this  purpose. 

Cylindrical  coils  may  also  be  so 
arranged,  in  that  the  coil  is  rotated 
about  its  axis,  the  turning  causing 

a  sliding  contact  to  move  up  and  down  along  its  length  as  in  the  Kohl- 
rausch  bridge  or  by  having  the  wire  of  the  coil,  which  is  bare  and  flexible, 
wound  and  unwound  to  any  desired  extent  on  a  bare  metallic  cylinder  or 
roll,  as  in  the  Wheatstone  resistances. 


FIG.  59. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       53 

The  arrangement  used  most  widely  for  gradual  variation  of  the 
self-induction  (called  "  variometer"  in  radio  practice)  consists  of  two  coils 
connected  either  in  series  or  in  parallel  and  whose  relative  position  to 


FIG.  60. 

each  other  may  be  varied.  Fig.  60  shows  a  variometer  designed  by  G. 
SEIBT  and  C.  LORENZ,  in  which  one  of  the  coils  is  turned  around  inside  of 
the  other.  The  self-induction  of  these  is  a  maximum  when  the  two  coils 
stand  parallel  to  each  other  and  the  current  flows  through  both  in  the  same 


FIG.  62. 


direction,  and  is  a  minimum  when  the  coils  are  still  parallel  but  carry  the 
current  in  opposite  directions.  Another  similar  method  is  sketched  in 
Fig.  61;  the  two  cylinders  shown  are  intended  to  be  placed  one  inside  of 
the  other,  one  of  them  being  turned  on  its  axis.  A  widely  used  arrange- 


54 


WIRELESS  TELEGRAPHY 


ment  is  shown  in  Fig.  236  (TELEFUNKEN*)  in  which  the  middle  one  of  the 
three  flat  coils  (marked  "28"  in  Fig.  236)  can  be  swung  from  side  to 
side.f 

A  particularly  elegant  construction  is  found  in  the  variometer  devised 

by  R.  RENDAHL  63  (Telefunken) .  Two 
flat  coils  wound  as  shown  in  Fig.  62 
are  mounted  face  to  face  on  a  common 
axis  (in  Fig.  62  they  are  shown  next 
to  each  other  instead  of  face  to  face) . 


FIG.  63. 


FIG.  64. 


One  of  them  turns  on  its  axis.  If  it  is  turned  so  that  those  halves  of  the 
two  coils  carrying  the  current  in  the  same  direction  are  superimposed, 
the  coefficient  of  self-induction  will  be  at  its  maximum.  If  turned  180° 

from  this  position,  the  coefficient  of  self- 
induction  becomes  a  minimum.  The 
advantage  of  this  variometer  lies  in  its 
compactness  (Fig.  63  shows  the  manu- 
factured instrument  for  heavy  currents 
and  rather  high  potentials)  and  in  the 
low  stray  magnetic  field  outside  of  the 
coils;  by  alternate  series  and  parallel 
connection  of  the  coils  a  very  wide  range 
in  the  self-induction  can  be  obtained. 

39.  Condensers  of  Constant  Capac- 
ity.52— a.  Plate  Condensers. — Plate  con- 
densers for  large  capacities  with  paper 
as  the  dielectric  are  adaptable  only  for 
low  voltages,  unless  a  sufficient  number 
are  joined  in  series.  Otherwise  mica 
(Fig.  64)  or  glass  plate  condensers  with 
coatings  of  tin-foil  or  thin  sheet  metal 
are  used.  Mica  as  the  insulating  mate- 

" Telefunken"  is  the  trade-name  of  the  German  Company  of  Wireless  Teleg- 
raphy— "  Gesellschaft  fuer  drahtlose  Telegrafie,  m.b.H.,"  Berlin. 

t  Translator's  Note:    This  is  sometimes  referred  to  as  the  "butterfly"  type  of 
variometer  coil. 


FIG.  65. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       55 


rial,  in  view  of  its  very  high  resistance  and  its  comparatively  high  di- 
electric constant,  permits  of  very  small  dimensions*  but  causes  quite  heavy 
losses  through  dielectric  hysteresis  if  the  load  is  not  kept  very  low. 
If  the  condenser  losses  are  to  be  minimized,  air  or  oil  must  be  used  as 


FIG.  66. 

the  insulating  material.  Two  constructions  of  air  condensers  are  shown 
in  Fig.  65  (GIEBE)  and  Fig.  66  (E.  HUTH)  respectively.  A  somewhat 
different  arrangement  is  shown  diagrammatic  ally  in  Fig.  67  for  an  oil 
condenser  as  designed  by  J.  A.  FLEMING.  With  air  condensers  great  care 
must  be  taken  that  the  advantage  of  practically  no 
energy  dissipation  is  not  lost  by  leakage  discharge 
(of  the  first  kind  described  in  [Art.  14o])  or  poor  in- 
sulation of  the  non-conducting  parts  which  serve 
to  hold  the  plates  in  position.  It  is  advisable  to 
enclose  these  condensers  in  containers  of  glass  or 
the  like  and  to  dry  the  air  within  thoroughly  by 
means  of  metallic  sodium. 

An  air  condenser  for  high  pressures  (compressed 
air  condenser)  as  built  by  the  National  Electric  Sig- 
nalling Co.,  at  the  suggestion  of  R.  A.  FESSENDEN 
is  represented  in  Figs.  68  and  69.  (See  b  for  the  ad- 
vantages of  compressed  air.) 

b.  Cylindrical  condensers. 

The  best-known  form  of  cylindrical  condenser,  the  Leyden  (also  the 

*  The  dimensions  of  a  mica  condenser  for  a  breakdown  potential  of  1000-1500 
volts  for  example  are  26  X  54  X  8  mm.  for  about  0.01  MF.,  26  X  54  X  14  mm.  for 
about  0.2  MF.  (C.  LORENZ). 


FIG.  67. 


56 


WIRELESS  TELEGRAPHY 


Kleit)  jar,  has  glass  for  its  dielectric.  Glass  is  chosen  in  view  of  its 
low  (dielectric)  hysteresis  losses  and  its  low  conductivity,  while  the  form 
of  the  jar  is  chosen  on  account  of  its  low  leakage  discharge  [Art.  86]. 
In  this  connection  a  long  narrow  form  of  jar  is  always  the  most  ad- 
vantageous (note  the  battery  of  jars,  as  built  by  TELEFUNKEN,  in  Fig. 
70). 

The  Leyden  jars  of  J.  MOSCICKI*  (Fig.  71)  in  which  the  upper  ends  are 
made  narrower  and  heavier  than  the  main  body  (Fig.  72)  are  particularly 


FIG.  68. 


FIG. 


effective  in  minimizing  the  leakage  discharge.  The  thickening  of  the 
glass  at  the  top  also  increases  the  breakdown  voltage  as  experience  has 
shown  that  Leyden  jars  mostly  break  down  at  the  top  edge  of  the  coatings. 
The  construction  of  these  jars  is  evident  from  Fig.  72,  in  which  PI 
and  P2  are  the  terminals  of  the  two  coatings,  L  is  a  metal  tube,  b  is  a 
rubber  stopper  and  /  is  a  porcelain  insulator.  The  coating  consists  of 
a  thin  layer  of  silver  chemically  deposited  and  covered  by  a  thicker 

*  Manufactured  by  Messrs.  WOHLLEBEN  &  WEBER,  in  Saarbriicken,  from  whose 
descriptive  pamphlets  Figs.  71  and  72a  and  b  are  taken.66 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       57 

layer  of  copper.  The  jars  are  filled  with  a  mixture  of  distilled  water 
and  glycerine  having  a  low  freezing  point  and  serving  to  secure  a  good 
contact  between  the  terminal  PI  and  the  inner  coating.  This  also  pre- 
vents a  too  rapid  heating  of  the  jar. 

Another  method  for  raising  the  breakdown  voltage  and  minimizing 


r\ 


V 

FIG.  72a.    FIG.  727>. 


FIG.  70. 


FIG.  73. 


the  effect  of  leakage  discharge  is  shown  in  Fig.  73  (Allgemeine  Elektri- 
zitatsgesellschaft).  The  dielectric  is  split  into  two  parts  at  the  top,  the 
outer  part  being  bent  out  like  an  umbrella. 

For  purposes  requiring  particularly  low  energy  loss  the  very  handy 
compressed  gas  condensers  as  designed  by  M.  WIENIT  are  very  conven- 
ient. Their  design  is  shown  in  Fig.  74.  The  use  of  carbonic  acid  gas, 


58 


S,     3 


Section  A-B 
FIG.  74. 


WIRELESS  TELEGRAPHY 

Volt 


4        6       8       10     12     U      16     18      20     22 
Pressure  in  Atmospheres 

FIG.  75. 


FIG.  76. 


FIG.  77. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       59 


under  a  pressure  of  twenty  atmospheres,  greatly  raises  the  breakdown 
voltage,  bringing  this  even  higher  than  for  oil  filling,  so  that  these 
condensers  may  be  used  without  difficulty  up  to  about  35,000  volts,  in 
spite  of  the  very  small  space  (3  mm.) 
between  the  cylinders.  (See  the  curve 
in  Fig.  75  for  the  relation  of  break- 
down voltage  to  gas  pressure  in  con- 
densers of  this  type.)  The  high  pres- 


FIG.  78. 


FIG.  79. 


sure  also  reduces  the  leakage  discharge  to  such  an  extent  that  it  has 
not  been  possible  to  measure  it  up  to  potentials  of  about  35,000  volts.57 

40.  Variable  Condensers.52 — Conden- 
sers whose  capacity  is  changed  in  steps,  as 
that  shown  in  Fig.  76,  are  seldom  used. 
Instead  of  this,  it  is  customary  to  use  bat- 


y 


FIG.  80. 


teries  of  Leyden  jars,  and  vary  their  number  according  to  the  required 
capacity. 

a.  Continuous  variation  in  the  capacity  of  condensers  is  usually  ac- 


60 


WIRELESS  TELEGRAPHY 


complished  by  varying  the  relative  position  of  the  two  coatings  or  con- 
ducting plates.  This  form  of  condenser  was  probably  first  introduced 
into  radio  practice  by  A.  KopSEL57ain  the  form  represented  by  Fig.  77. 

The  conducting  elements  are  made 
up  of  sets  of  semicircular  plates  or 
discs  of  which  one  is  stationary  and 
the  other  rotated  into  the  spaces 
between  the  plates  of  the  former. 
A  pointer  moving  over  a  circular 
scale  (see  Fig.  77)  indicates  the  po- 
sition of  the  movable  element.  The 
first  form  of  this  type  of  condenser 
built  by  TELEFTJNKEN  is  shown  in 
Fig.  78.  They  are  now  made  by 
many  firms.  For  instance,  Fig.  79 
shows  a  construction  developed  by 
C.  LORENZ,  Fig.  80  represents  a  precision  condenser  of  G.  SEIBT,  and 
Figs.  81  and  82  show  an  arrangement  with  vertical  plates  made  by 
C.  LORENZ.  The  latter  is  said  to  allow  of  a  better  circulation  of  the 


FIG.  81. 


oil  and  to  prevent  air  bubbles  from  collecting  on  the  plates.  The  con- 
denser plates  as  made  by  H.  BOAS  (Fig.  83)  are  also  vertical,  but  cylin- 
drical in  shape. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       61 


The  desire  to  combine  maximum  capacity  with  minimum  space 
underlies  the  design  of  Fig.  84,  C.  LORENZ.  It  consists  of  a  combination 
of  two  (or  three)  condensers  of  the  form  of  Fig.  77  in  such  manner  that 
the  two  movable  sections  g  and  h  occupy  a  common  space  in  one  position. 


FIG.  83. 


The  problem  of  minimizing  space  is  solved  with  particular  nicety  in 
the  condensers  of  the  Marconi  Co.  These  also  have  the  movable  section 
made  up  of  semicircular  plates,  similar  to  those  of  Fig.  77,  but  differ 


FIG.  85. 


in  having  two  stationary  (AiA2,  Fig.  85)  and  two  rotating  (B iB2,  Fig. 
85)  sections  arranged  as  shown.  One  stationary  and  one  rotating 
set,  say  AI  and  J5i,are  connected  to  one  terminal,  while  the  others,  A2 
and  B2,  are  joined  to  the  other  pole.  Then  the  capacity  is  greatest 


62 


WIRELESS  TELEGRAPHY 


when  BI  entirely  covers  A2)  B%  covering  A\.  This  capacity,  for  the  same 
total  volume  occupied  and  the  same  distance  between  plates,  is  double 
that  of  a  similar  condenser  having  only  one  stationary  and  one  movable 
section  of  plates. 

2.  CURRENT  AND  VOLTAGE 


41.  Relation    between    Current    and    Voltage  Amplitudes 

undamped  sinusoidal  oscillations  the  relation  is  given  by 


7o  = 


For 


(1) 


in  which  R  and  L  are  the  resistance  and  co- 
efficient of  self-induction  respectively  of  the 
circuit  whose  end-points  have  a  difference  of 
potential  F0. 

For  damped  oscillations  within  the  limits 
encountered  in  practice,*  this  relation  also 
holds  approximately.  It  assumes  an  even 
simpler  form  for  all  wire  circuits,  unless  these 
consist  of  particularly  thin  wires  of  low  con- 
ductivity, as  in  these  the  inductance,  in  view 
of  the  high  frequencies  customary  in  radio 
practice,  increases  much  more  rapidly  than 
the  resistance.  We  may  therefore  write  ap- 
proximately : 


/o  = 


(2) 


b.  If  a  current  /  (Fig.  86)  divides  itself  into  two  paths  one  having  a 
resistance  ^i  and  a  coefficient  of  self-induction  LI,  the  constants  of  the 
other  being  R2  and  L2,  then  we  have  for  the  ratio  of  the  currents  I\  and  1 2 
in  each  of  the  parallel  paths 

(3) 


+ 

If  both  branches  are  made  of  fairly  heavy  wire,  then  the  lower  the 
resistance  is  in  comparison  to  the  inductance,  the  more  nearly  accurate 
will  be  the  approximate  relation 


so  that  the  splitting  of  the  current  depends  not  upon  the  resistance  but 
upon  the  coefficients  of  self-induction  of  the  branches. 

*  i.e.,  d  is  much  less  than  2ir. 

t  It  is  assumed  that  the  two  branches  do  not  affect  each  other  inductively. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT      63 

The  two  branches  may  be  intentionally  so  adjusted  that  the  resistance 
of  one  of  them,  say  Ri,  is  much  greater  than  its  self-induction  while  the 
reverse  is  true  of  the  other  branch.  We  then  have: 


/20  I-leff  Rl 

This  gives  a  simple  measure  of  w  and  the  frequency  N*  from  the  ratio  of 
the  branch  currents. 

It  has  been  frequently  suggested  to  make  use  of  this  relation  for 
measuring  the  frequency  by  noting  the  current  indicated  by  ammeters,  A  i 
and  A  2,  in  each  branch  circuit.  This  scheme  is  very  neatly  carried  out  in 


FIG.  87. 

FERRIE'S    "frequency-meter,"    which    gives    direct    readings    of    the 
frequency.62 

The  two  ammeters  are  so  arranged  that  their  pointers  AI  Zi  and  A2Z2 
(Fig:  87)  cross  each  other.  At  a  given  frequency,  N ,  for  any  deflection, 
«i,  of  the  pointer  of  AI  only  one  definite  deflection,  «2,  of  the  other 
instrument,  A2,  will  correspond,  so  that  the  pointers  will  intersect  at  a 
definite  point.  For  another  current  of  the  same  frequency  passing 
through  the  system,  other  deflections,  /?i  and  (32  (dotted  lines  in  Fig.  87), 
and  another  definite  point  of  intersection  correspond.  By  thus  varying 
the  current  at  a  constant  frequency,  the  successive  points  of  intersection 
develop  a  curve  (/  in  Fig.  87)  which  geometrically  locates  the  frequency 
N  on  the  face  of  the  instrument.  By  repeating  this  process  with  other 
frequencies,  individual  curves  (II,  III,  etc.,  Fig.  87)  are  obtained  for  each 
frequency.  These  curves  once  determined  to  measure  an  unknown 

*  The  same  in  fact  is  true  of  the  more  general  equation  (3). 


64  WIRELESS  TELEGRAPHY 

frequency  it  is  only  necessary  to  observe  on  which  curve  the  instrument 
pointers  intersect,  which  will  indicate  the  desired  frequency. 

If  one  of  the  paths  contains  a  coil  of  very  high  self-induction,  while  the 
other  path  contains  neither  high  self-induction  nor  high  resistance,  then 
the  oscillations  will  flow  through  the  second  path  almost  entirely.  The 
first  path  is  said  to  be  " choked"  (high  frequency  "choke  coil"). 

c.  In  applying  equation  (2)   to  an  entire  condenser  circuit  (AFB, 
Fig.   1)   the  difference  of  potential  between  the    condenser    coatings* 
must  be  taken  for  V  and  the  coefficient  of  self-induction  of  the  entire 
circuit  substituted  for  L. 

If  capacity  is  introduced  in  place  of  self -inductance,  we  have: 

Jo  =  coC.Fo63  (4) 

To  illustrate  the  application  of  this  formula,  consider  the  condenser 
circuit  formerly  installed  at  the  German  station  in  Nauen  (TELEFUNKEN). 
Its  effective  capacity  was  0.44  MF.,  the  frequency  about  1.5  X  105/sec. 
With  60,000  terminal  volts,  we  have 

7o  =  27T  X  1.5  X  105  X  0.44  X  10~15  X  60,000  C.G.S.  units 
=  approx.  2500  C.G.S.  units  =  25,000  amp. 

It  should  be  noted  that  the  current  amplitude  is  very  great,  even  from 
the  standpoint  of  commercial  light  and  power  circuits. 

d.  Equation  (4)  holds  in  general  for  any  condenser  in  the  circuit,  if 
C  is  its  capacity,  V  the  potential  difference  of  its  coatingsvand  7  is  the 
current  in  the  circuit.     If  the  capacity  C  is  very  great,  F0  becomes  very 
small ;  in  this  case  the  condenser  acts  as  a  short  circuit  for  the  oscillations, 
while  it  would  offer  an  infinitely  great  resistance  to  a  direct  current. 
It  may  therefore  be  used  to  "block"  or  protect  the  circuit  against  a  direct 
current  without  appreciably  affecting  the  oscillations. 

42.  The  Breakdown  Voltage  and  Gap  Length.64 — A  given  voltage, 
V,  say  that  existing  across  the  plates  of  a  condenser,  may  be  measured 
by  its  "breakdown  gap"  i.e.,  the  length  of  a  gap  in  air  or  gas  over  which 
the  voltage  V  would  just  discharge  itself. f  The  relation  between  the 
length  of  the  gap  and  the  breakdown  potential  depends  on  the  form 
of  the  electrodes  (on  their  radius  in  case  of  spheres),  on  the  particular 
kind  of  gas  in  the  gap  as  well  as  its  condition,  and  the  method  of  charg- 
ing the  electrodes,  i.e.,  whether  a  static  charge  has  been  supplied  by  a 
friction  or  influence  machine,  or  whether  the  charge  is  produced  by  os- 
cillations or  by  an  induction  coil. 

*  For  several  condensers  in  series  this  would  be  the  sum  of  their  potential 
differences. 

t  This  is  also  known  under  various  other  names  such  as  "discharge  voltage,"  "rup- 
ture voltage,"  and  is  also  identical  with  the  "ignition  voltage,"  Vzt  mentioned  in 
Art.  129. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       65 

a.  The  relation  of  gap  length  and  breakdown  voltage  for   air   and 
static  charges  is  given  in  Table  IX. 

From  these  curves  it  will  be  noted  that  for  short  gaps  the  size  of  the 
electrode  (radius  of  the  sphere)  has  but  little  effect.  Its  importance  in- 
creases, however,  with  each  increase  in  gap  length,  so  that  with  very 
small  spheres  the  breakdown  voltage  increases  only  very  slowly  for 
increasing  gap  length,  while  with  large  spheres  it  remains  in  approxi- 
mate proportion  to  the  gap  length  up  to  much  greater  distances.  With 
plate  or  disc  electrodes  (Fig.  88)  the  relations  are 
similar  to  those  for  spheres  of  very  large  diameter. 

b.  If  the  charge  on  the  electrodes  is  produced 
by    oscillations,    the    relation   between  breakdown 
potential  and  gap  length  is  also  affected  by  the  fre- 
quency.    The    higher    the   frequency,    the   higher 

is    the   voltage  necessary  to  jump  a  gap  of  given  FIG.  88. 

length.65 

This  is  due  to  the  fact  that  when  the  voltage  is  reached  at  which  a 
discharge  would  finally  occur  if  this  voltage  were  maintained,  i.e.,  the 
normal  breakdown  voltage  (Table  IX),  the  discharge  does  not  take  place 
immediately  and  the  voltage  will  have  risen  above  the  normal  dis- 
charge value  at  the  instant  at  which  the  discharge  actually  takes  place.* 
This  phenomenon  is  called  "retardation"  or  "lag  of  the  discharge" 
(E.  WARBURG).66  It  plays  an  important  part  in  wireless  telegraphy, 
as  in  radio  practice  the  high  potential  usually  exists  only  for  very  brief 
periods  (e.g.,  in  induction  coil  interrupters,  alternating-current  transformers 
and  even  more  so  with  high  frequency  oscillations).  The  cause  of 
this  phenomenon  lies  in  the  low  number  of  ions  contained  by  the  gas  in 
the  gap.  Its  occurrence  can  be  prevented  by  providing  a  sufficient 
quantity  of  ions  in  the  gas.  This  is  most  easily  attained  by  subjecting 
the  negative  electrode  (both  electrodes  in  the  case  of  alternating-current 
operation)  to  ultraviolet  light,  thereby  inducing  the  emission  of  negative 
electrons.  This  method  is  advisable  wherever  it  is  important  that  the 
spark  discharge  occur  always  at  the  same  potential.  In  fact,  if  properly 
applied  even  for  radio  frequencies  the  breakdown  voltages  and  gaps 
will  be  practically  the  same  as  for  static  charging,  and  the  values  of 
Table  IX  may  be  applied  without  appreciable  error.65 

c.  The  discharge  voltage  is  reduced  under  the  conditions  encountered 
in  radio  practice  by  heating  the  electrodes,  in  fact  by  any  strong  ioni- 
zation   of   the  gas.     In  practice  ionization  is  usually  produced  by  im- 
mediately preceding  discharges.     If  a  number  of  spark  discharges  are 
passed  over  a  gap  in  rapid  succession,  the  voltage  may  be  reduced  very 
considerably  from  that  required  for  the  initial  discharge. 

The  breakdown  potential  may  be  increased  by  raising  the  pressure 

*  Apparently  the  phenomenon  described  in  c  is  also  due  to  this  condition. 


66 


WIRELESS  TELEGRAPHY 


above  atmospheric.  Up  to  about  10  atmospheres  the  discharge  voltage 
is  approximately  proportional  to  the  pressure  [see  Art.  396]. 

The  breakdown  potential  is  not  much  different  for  various  gases 
such  as  air,  nitrogen,  oxygen,  carbon  dioxide,  etc.  However,  it  is  only 
about  one-half  as  great  for  hydrogen  as  for  those  mentioned,  and  much 
lower  still  for  helium  and  argon. 

d.  So-called  "micrometer  gaps"  as  illustrated  in  Fig.  89  serve  for 
measuring  the  breakdown  gap.  KiK%  are  the  spherical  electrodes,  GiG$ 
good  insulators  of  glass  or,  better  yet,  porcelain,  Si  a  micrometer  screw, 
Sz  the  lever  head  of  a  set  screw,  not  otherwise  visible  in  the  illustration. 
If  S2  is  loosened  the  electrode  on  the  left  can  be  moved  away  from  or 
nearer  to  the  other  electrode,  while  the  micrometer  screw,  Si,  serves  for 
the  fine  adjustments. 


FIG. 


The  radius  of  the  spheres  Ki  and  K%  should  be  chosen  at  least  as 
great  as  the  gap  length  being  measured.  Moreover,  the  field  between  the 
electrodes  must  not  be  disturbed  by  any  conductors  in  its  vicinity  if 
results  for  general  comparison  are  desired  and  the  values  of  Table  IX 
are  to  be  used. 

43.  Insulation  of  Conductors. — a.  In  view  of  the  high  voltages  which 
occur  when  working  with  damped  oscillations,  there  is  often  great  danger 
of  a  spark  discharge  between  two  points  of  the  circuit.  Hence  the  con- 
ducting circuit  must  be  carefully  insulated  against  spark  discharges.  For 
example,  if  a  spark  jumps  across  from  A  to  B  in  the  condenser  circuit 
shown  in  Fig.  90,  practically  the  entire  current  will  flow  via  AFiB, 
as  this  path  offers  a  much  lower  impedance  than  the  path  ADB,  and 
thus  the  entire  oscillation  will  be  changed. 

6,  On  the   other  hand,  insulation  against  current  losses  in   circuits 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       67 


To  Induction  Coil 


charged  by  damped  oscillations  is  not  so  essential67  as  it  is  for  high  tension 
direct  current  or  commercial  alternating  current  or  even  for  undamped 
high  frequency  current. 

For  instance,  if  A  and  B  in  Fig.  90  were  joined  by  a  poor  insulator,  say 
a  wooden  strip,  this  would  not  perceptibly  impair  the  oscillations,  in 
spite  of  the  high  voltage  developed  between  A  and  B,  for  the  length  of 
time  during  which  the  potential  between  A  and  B  is  at  all  high  is  so  short 
for  damped  oscillations  of  such  decrements  as  come  into  question  in 
practice  that  the  loss  across  the  strip  of  wood  becomes  very  small — 
unless  the  number  of  discharges  per  second  is 
extremely  great. 

Nevertheless,  to  insure  against  unnecessary 
energy  losses  the  best  insulating  materials 
(porcelain  and,  second  in  rank,  oil  and  hard 
rubber)  should  always  be  used. 

c.  All  parts  subjected  to  high  voltages 
from  the  induction  coil  or  transformer  must 
be  insulated  with  the  greatest  care,  otherwise 
very  heavy  losses  may  result.67  In  circuits 
having  several  condensers  in  series,  only  the 
portions  FCi  and  FC2  (Fig.  11)  require  heavy 
insulation;  but  if  there  is  only  one  condenser 
or  there  are  several  in  parallel  in  the  circuit, 

then  the  entire  circuit  requires  careful  insulation.  In  this  respect  the 
connection  of  condensers  in  series  may  at  times  offer  a  considerable 
advantage. 

3.  MEASUREMENT  OF  CURRENT 

44.  The  Indications  of  Hot-wire  Instruments. — a.  Under  hot-wire 
instruments,  in  the  broadest  sense,  should  be  understood  those  instru- 
ments whose  deflection  is  caused  by  the  development  of  heat  due  to  the 
current  passing  through  a  wire. 

The  deflection  of  such  an  instrument  is  a  measure  of  the  average 
quantity  of  heat,  Q,  *  developed  per  second.  In  general,  the  heat  developed 
per  second  in  a  wire  of  effective  resistance  R  is 

in  which  Peff  is  the  mean  value  of  72,  the  current  effect.68 

For  undamped  sinusoidal  oscillations 


smm 


D 

FIG.  90. 


i\tt  = 


(2) 


so  that 


Q-i 


*  The  deflection  need  not  be  proportional  to  Q,  but  is  approximately  so  in  most 
instruments. 


68  WIRELESS  TELEGRAPHY 

For  damped  oscillations  whose  amplitude  curve  is  of  the  exponential 
form,  the  heat  developed  during  one  discharge 

7?^ 

K4Nd 

If  then  there  are  £  discharges  per  second,  the  total  quantity  of  heat 
developed  in  1  second 

o2  (3) 


Comparing  this  with  equation  (1)  we  obtain 

•/«.//  -ifew  (4) 

For  damped  oscillations  whose  amplitude  curve  is  a  straight  line10 


in  which  a  is  the  lineal  decrement  [Art.  9a]. 

6.  As  the  effective  resistance,  R,  of  a  wire  depends  on  the  frequency, 
the  same  is  true  of  the  indications  of  hot-wire  instruments.  These, 
however,  can  be  made  independent  of  the  frequency  (also  usually  making 
calibration  with  direct  current  possible  at  the  same  time)  by  the  use  of 
very  thin  wires  [Art.  366]  whose  diameter  is  less  than  that  given  in 
Table  VIII.* 

c.  A  hot-wire  instrument  calibrated  with  direct  current  gives  direct 
readings  for  the  current  amplitudes  of  undamped  oscillations,  if  the  latter 
are  approximately  sinusoidal  [equation  (2)]. 

This  is  not  the  case  with  damped  oscillations,  as  here  not  only  the 
current  amplitude  but  also  the  decrement,  d,  the  frequency,  N,  and  the 
number  of  discharges  per  second,  f  ,  enter  as  factors  [equation  (3)].  Only 
when  these  are  known  is  it  possible  to  calculate  the  current  amplitude 
from  the  indication  of  a  hot-wire  instrument. 

d.  A  method  for  determining  the  frequency  and  the  decrement  for 
the  case  of  exponential  decrease  of  the  amplitude  will  be  given  later 
[Art.  74,  et  seq.].     The  number  of  discharges  per  second,  when  using 
induction  coils  or  some  form  of  motor-driven  interrupter,  is  easily  de- 
termined from  the  speed,  on  condition  that  each  interruption  corresponds 
to   only   one   discharge,   so   that   the  number  of  interruptions  and  the 
number  of  discharges  are  identical.     The  same  relation  holds  between  the 
number  of  alternations  and  the  number  of  discharges  when  operating 
with  alternating  current.     In  general,  the  number  of  discharges  and  the 
number  of  interruptions  (or  of  alternations)  are  not  identical.     If  the 

*  The  instrument's  independence  of  the  frequency  is  again  destroyed  as  soon  as 
a  shunt  is  connected  to  the  instrument  for  adjusting  its  sensibility. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       69 


primary  current  is  sufficiently  strong,  each  interruption  (or  each  half 
period  of  alternating  current)  will  be  accompanied  by  several  "partial 
discharges"  or  "partial  sparks."  Whether  or  not  this  is  occurring  is 
easily  determined  by  observing  the  spark  image  in  a  rotating  mirror. 
If  this  appears  as  shown  in  the  photograph  reproduced  in  Fig.  91,  there 


FIG.  91. 

are  no  partial  discharges,  while  an  image  as  shown  in  Fig.  92  indicates 
the  presence  of  partial  discharges.* 

If  the  image  of  the  spark  gap  in  a  rotating  mirror  is  photographed, 


FIG.  92. 

then  the  number  of  discharges  per  second  can  be  calculated  from  the 
distance  between  the  successive  images  on  the  photograph,  the  speed  of 
the  mirror  and  the  dimensions  of  the  outfit.  If  the  spark  itself  is  in- 
visible, an  oscillograph  (with  incandescent  lamp)  or  a  Braun  tube  can  be 
used  in  conjunction  with  a  rotating  mirror  to 
count  the  discharge  frequency.  A  more  conven- 
ient indicator  for  this  purpose  is  the  discharge 
analyzer 'f  of  J.  A.  FLEMING,  which  consists  of 
a  GEISSLER  (helium  or  neon)  tube  attached  to 
the  armature  of  a  small  motor. 

Fig.  93  shows  the  construction,  Fig.  94  a 
finished  instrument,  as  made  by  C.  LORENZ.  If 
the  two  terminals  P\  and  P%  are  respectively 
connected  to  two  points  of  a  condenser  circuit 
or  other  oscillator,  a  high  frequency  current  will 
pass  through  the  helium  tube  (d,  Fig.  93 1)  which 
lights  at  each  discharge.  The  speed  of  the  motor 
is  regulated  to  a  point  at  which  the  image  of 

the  tube  appears  stationary  to  the  eye.     If  it  appears  as  shown  in  Fig. 
95,  it  follows  that  there  are  four  discharges  during  every  complete  revo- 

*  With  a  little  practice  this  can  also  be  determined  from  the  sound  of  the  spark, 
which  for  partial  discharges  tends  to  become  hissing  rather  than  crackling. 

t  Also  frequently  called  "oscillation  analyzer." 

t  The  metal  rings  m  and  n  form  the  electrodes  of  a  condenser,  the  rings  k  and  i 
forming  another.  The  tube  is  connected  between  these  two. 


FIG.  93. 


70 


WIRELESS  TELEGRAPHY 


lution  of  the  motor,510  while  if  it  has  the  appearance  of  Fig.  96,  there 
are  four  groups  of  three  partial  discharges  each  per  revolution. 


FIG.  94. 


FIG.  95. 


FIG.  96. 


To  Oscillator 
FIG.  97. 


Another  simple  and  convenient  method  is  that  sketched  in  Fig.  97. 71 
On  the  shaft  of  a  small  motor  a  photographic  plate  or  film,  P,  is  at- 
tached.    Very  near  to  this  is  a  metallic  point,  S,  which  is  conductively 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       71 

connected  to  a  point  of  the  oscillator  and  is  quickly  moved  across  the 
plate  by  means  of  the  handle  H.  Each  oscillation  is  accompanied  by  a 
discharge  between  the  point  S  and  the  plate,  which,  when  developed, 
shows  a  series  of  dark  points  arranged  on  a  spiral,  each  point  represent- 
ing a  discharge.  From  these  points,  knowing  the  speed  of  the  motor, 
the  number  of  discharges  per  second  is  easily  obtained,  independently 
of  the  velocity  at  which  S  is  moved  over  P. 

45.  Commercial  Hot-wire  Instruments. — Some  hot-wire  ammeters 
may  be  used  for  high  frequency  oscillations,  without  any  shunt.  It 
is  preferable,  however,  to  use  instruments  especially  made  for  high  fre- 
quency currents,  as  those,  for  instance,  of  HARTMANN  AND  BRAUN72 
(FRANKFORT  A.  M.,  Bockenheim,  Germany). 

The  type  shown  in  Fig.  98  is  intended  for  heavy  currents,  that 


FIG.  98. 


shown  in  Fig.  99  being  designed  for  a  minimum  energy  consumption. 
The  scale  of  the  former  gives  the  value  of  Ie/f  in  amperes,  while  the  latter 
indicates  the  energy  used  in  the  instrument  in  watts,*  which  is  propor- 
tional to  Peff.  In  the  latest  and  most  sensitive  instruments  of  this 
type,  the  energy  consumed  amounts  to  only  about  0.015  watt. 

46.  The  Hot-wire  Air  Thermometer. — The  air  thermometer  or  hot- 
wire air  thermometer  devised  by  RIESS  (Figs.  100  and  101)  and  brought 
into  radio  practice  by  F.  BRAUN  is  a  particularly  simple  laboratory 
instrument.  It  consists  of  a  glass  cylinder  provided  with  an  alcohol 
manometer  and  a  glass  stopcock,  by  means  of  which  the  difference  be- 
tween the  pressure  within  and  the  outside  atmospheric  pressure  can  be 

*  This  is  not  a  sufficient  excuse  for  the  common  misnomer  of  "hot-wire  wattmeter" 
so  frequently  applied  to  this  instrument. 


72 


WIRELESS  TELEGRAPHY 


equalized.  The  hot  wire,  H,  is  at  the  bottom  of  the  glass  cylinder,73  be- 
tween two  heavy  entrance  wires  which  are  led  in  through  a  stopper, 
the  glass  cylinder  usually  being  surrounded  by  a  vacuum  chamber  and 
sometimes  in  addition  by  a  silver  coating.  Current  passing  through  H 
heats  this  and  also  the  air  in  the  glass  cylinder,  causing  an  increase  in 
the  pressure,  which  is  indicated  by  the  manometer.  These  instru- 
ments are  best  calibrated  with  direct  current. 

47.  Bolometer,  Barretter.74 — The  hot  wire,  w,  in  Fig.  102  is  con- 
nected as  one  arm  of  a  Wheatstone  Bridge, 
which  is  adjusted  until  no  current  flows 
through  the  galvanometer,  g.  If  now  we  send 
an  alternating  current,  i,  through  w  (AB), 
this  wire  becomes  hot  and  its  resistance  in- 
creases, and  the  galvanometer  deflection  caused 
thereby  is  pretty  nearly  in  exact  proportion 
to  the  current  effect  of  i. 

A  somewhat  different  arrangement  of  this 
device,  which  is  called  a  bolometer,  is  shown 
in  Fig.  103.  The  branches  pqrs  and  piqtfiSi 
which  replace  w  and  c  in  Fig.  102,  respectively, 
are  made  of  thin  iron  or  platinum  wire  and  as 
nearly  alike  as  possible,  and  the  arms  pqr  and 
s  are  so  equalized  that  if  direct  current  is  ap- 
plied at  E  and  F,  the  galvanometer  g  shows 
no  deflection,  so  that  the  points  C  and  D  have 
the  same  potential  with  direct  current. 

This  arrangement  has  the  following  advan- 
tages: (1)  The  bolometer  is  less  affected  by 
variations  in  the  room  temperature,  as  pqrs 
and  piqiTiSi  are  subjected  to  the  same  influ- 
ence; (2)  at  most,  only  a  very  small  portion  of 
the  alternating  current  led  in  through  A  and 

B  flows  into  the  other  circuits  of  the  bridge  or  into  the  galvanometer,* 
as  the  points  C  and  D  remain  at  practically  equal  potential  even  with  a 
variable  current. 

On  the  other  hand,  the  simpler  arrangement  shown  in  Fig.  102  has 
the  advantage  that  the  hot  wire  can  easily  be  put  into  a  vacuum  in  a 
glass  tube.  This  greatly  reduces  the  heat  lost  by  convection,  consider- 
ably increasing  the  sensitiveness  (FESSENDEN,  TISSOT).  Similarly,  the 
use  of  extremely  thin  wires  in  this  arrangement  is  advantageous  as  com- 
pared to  the  method  of  Fig.  103.  This  also  tends  toward  high  sensi- 
tiveness. The  calibration  curve  shown  in  Fig.  104  is  that  of  a  bolometer 

*  Choke  coils  must  be  connected  at  each  end  of  the  hot  wire  for  this  purpose  in 
the  arrangement  of  Fig.  102.  * 


FIG.  100. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       73 


of  BELA  GATi,74  having  a  gold  wire*  of  0.002  to  0.003  mm.  diam.,  while 
a  bolometer  with  a  0.0005  platinum  wire  gave  a  deflection  of  ten  scale 
divisions  for  0.034  milliampere,  with  the  same  galvanometer.  B.  S. 


FIG.  101. 


CoHEN74  was  able  to  measure  currents  as  low  as  5  X  10  3  milliamperes 
by  means  of  a  carbon  filament  in  a  vacuum. 


FIG.  103. 


*  Galvanometer  =  movable  coil  galvanometer,  direct  reading;  one  scale  division  = 
1  X  10~6  amp.  BELA  GATI  makes  use  of  a  special  compensation  method  of  connection 
instead  of  the  complete  bridge  arrangement.  Using  a  single  pivot  galvanometer 
made  by  PAUL  (London)  (1°  =  1 X  10~7  amp.)  he  obtained  a  deflection  of  5°  at  0.001 
milliampere  with  the  0.0005  mm.  platinum  bolometer. 


74 


WIRELESS  TELEGRAPHY 


48.  Thermoelement75  or  Thermocouple. — a.  KLEMENCIC  adopted 
the  form  illustrated  in  Fig.  105*  for  the  thermoelements  used  in  the 
measurement  of  electric  oscillations.  A  and  B  are  thick  wires  through 

which  the  oscillations  are  led  in, 
while  the  wires  c  and  d  connect  to 
a  galvanometer.  ai«2  and  6i&2  are 
very  thin  wires  of  different  mate- 


rial   (e.g.,   constantan  and  iron  or 


1.2 


0.8 


0.0 


0.4 


0.2 


0  10         20          30          40          50 

~*"~      Galvanometer  Scale  Divisions 

FIG.  104. 


FIG.  105. 


constantan  and  platinum).  If  oscillations  pass  through  the  wires  AB, 
the  wires  6ia2  become  heated  as  do  also  the  points  of  contact  of  the 
wires  ai«2  and  &i&2,  the  heat  developed  at  these  points  of  contact  being 


FIG.  106. 


FIG.  107. 


greater  than  at  the  soldered  points  a^c  and  bzd.     This  uneven  heating 
produces  a  thermoelectric  EMF  and  a  deflection  of  the  galvanometer. 

*  Greatly  enlarged. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT       75 


b.  The  sensitiveness  of  these  thermoelements  is  greatly  increased 
by  enclosing  them  in  a  high  vacuum,  as  shown  by  P.  LEBEDEW.     H. 
BRANDES75  has  designed  a  very  simple  construction  for  this,  shown  in 
Fig.  107,  while  Fig.  106  shows  a  diagrammatic  cross-section  through  two 
of  the  four  wires.* 

A  particularly  good  thermoelement  is  obtained  by  the  combination 
of  tellurium  with  constantan  or  tellurium  with  platinum  (say  a  thin 
platinum  wire  sweated  on  to  a  small  ball  of  tellurium)  (L.  W.  AUSTIN). 75 

c.  An  advantage  of  the  thermoelement  as  compared  to  the  bolometer 
is  that  no  auxiliary  cell  (e,  Fig.  103)  and  no  equal- 
izing of  the  bridge  are  necessary. 

Both  bolometer  and  thermoelement  require  only 
a  very  small  amount  of  heat  and  hence  only  a  very 
small  amount  of  energy  to  produce  a  considerable 
deflection,  particularly  if  a  highly  sensitive  galvan- 
ometer is  used,  wherein  lies  their  great  advantage 
over  hot-wire  air  thermometers  or  the  commercial 
hot-wire  instruments.  For  many  purposes  the  very 
convenient  direct-reading  movable  coil  galvanom- 
eters are  sufficient;  however,  if  measurements  neces- 
sitating the  lowest  possible  energy  consumption  are 
to  be  made,  a  good  mirror  galvanometer,  not  too 
extremely  damped,  is  more  suitable. 

Calibration  of  these  is  best  obtained  with  alter- 
nating current  and  an  electrodynamic  precision  volt- 
meter without  a  multiplier. 

49.  The  Thermogal variometer. — There  is  one  in- 
strument even  more  sensitive  than  either  the  ther- 
moelement or  the  bolometer  of  usual  design,  viz., 
the  thermogalvanometer,  constructed  by  H.  DUD- 
DELL76  following  an  arrangement  of  C.  V.  BOYS  for 
measurements  with  high  frequency  oscillations. 

The  principle  is  as  follows:  Between  the  poles  N  and  S  (Fig.  108) 
of  a  horseshoe  magnet  a  movable  wire  frame  L  is  suspended  similarly 
to  a  movable  coil  galvanometer.  A  thermocouple  (antimony-bismuth) 
is  attached  at  the  lower  end  of  the  suspended  frame,  giving  a  very  high 
EMF.  At  one  junction  point  a  hot  wire  or  thin  strip  of  gold-leaf  or  strip 
of  a  platinum  mirror  on  glass  is  attached,  through  which  the  oscillations 
are  passed.  This  heats  the  strip  and  thereby  also  the  junction  point, 
producing  an  EMF  and  a  current  in  the  frame.  The  latter  is  thereby 

*  Thermoelements  and  bolometers  are  disadvantageous  when  a  vacuum  is  used, 
in  that  they  cannot  be  repaired  when  they  burn  out,  which  occurs  frequently  as  it 
is  difficult  to  provide  reliable  fuses.  When  no  vacuum  is  used,  it  is  a  simple  matter 
to  replace  the  burned  wire. 


76 


WIRELESS  TELEGRAPHY 


deflected  just  as  in  a  movable  coil  galvanometer,  a  mirror  and  scale 
serving  to  measure  the  deflection. 

Fig.  109  illustrates  a  construction  of  such  an  instrument*  said  to  be 
characterized  not  only  by  its  sensitiveness,  but  also  by  its  convenience. 

W.  GEKLACH77  has  devised  an  arrangement  similar  to  the  thermogal- 
vanometer,  having  the  highly  sensitive  thermocouple,  which  is  acted 
upon  by  the  hot-wire  strip,  connected  to  a  separate  sensitive  galvanometer. 

50.  Comparison  of  the  Sensitiveness  of  Various  Measuring  Instru- 
ments.78— The  following  table  gives  the  energy  consumption  at  a  deflec- 


FIG.  109. 

tion  of  100  mm.  or  100  scale  divisions  for  various  instruments,  this 
serving  as  a  measure  of  their  sensitiveness.  This,  however,  is  not  by  any 
means  a  measure  of  their  practical  usefulness,  which  depends  on  quite 
other  properties. 

51.  Measurement  of  Very  Small  Currents.79 — For  the  measurement 
of  very  small  currents  the  various  detectors  discussed  later  (e.g.,  galena- 

*  As  made  by  the  Cambridge  Scientific  Instrument  Co.     Figs.  108  and  109  are 
taken  from  a  pamphlet  issued  by  this  company. 


THE  HIGH  FREQUENCY  ALTERNATING-CURRENT  CIRCUIT      77 


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78  WIRELESS  TELEGRAPHY 

graphite  [Art.  150],  or  red  zinc  oxide-copper  pyrites  [Art.  160],  or  the 
audion  detector  [Art.  161  c])  can  be  used  to  advantage. 

They  are  used  in  connection  with  a  galvanometer  (arranged  for 
instance  as  shown  in  Fig.  375  in  the  circuit  $2C",  by  substituting  the 
galvanometer  for  the  telephone)  or  with  a  telephone  (as  in  Fig.  375).  In 
the  first  case  the  galvanometer  deflection  gives  a  direct  measure  of  the 
alternating  current*  passed  through  the  circuit,  while  in  the  second  case 
there  are  two  methods  for  arriving  at  the  current  value.* 

Either  an  adjustable  resistance  is  connected  in  parallel  to  the  telephone 
and  varied  until  the  sound  heard  in  the  telephone  becomes  just  audible — 
the  smaller  the  resistance  necessary,  the  greater  is  the  alternating  current 
measured — (the  so-called  "parallel-resistance"  method),  or  the  unknown 
alternating  current  is  caused  to  induce  current  through  an  adjustable 
coupling  [Art.  54]  in  a  circuit  containing  the  detector  and  telephone — 
the  looser  the  coupling  for  a  just  disappearing  sound,  the  greater  is  the 
measured  current. 

Such  devices  must  always  be  calibrated  before  being  used,  and  even 
then  are  adapted  for  accurate  measurements  only  if  the  detector  can  be 
relied  upon  for  entirely  constant  action.  Their  great  advantage,  however, 
lies  in  that  their  sensitiveness  is  of  quite  another  order79  than  that  of  the 
apparatus  described  in  Arts.  47-49. 

*  That  is,  the  effective  current  value,  when  thermodetectors  are  used. 


CHAPTER  IV 
COUPLED  CIRCUITS 

1.  COUPLING  IN  GENERAL 

62.  Magnetic,  Galvanic,  Electric  Coupling. — Two  electromagnetic 
systems  (oscillators  or  closed  current  circuits)  are  said  to  be  "coupled" 
if  they  are  so  arranged  that  oscillations  in  one  of  the  systems  always 
cause  oscillations  in  the  other.  That  system  or  circuit  in  which  the 
energy  is  first  supplied,  say  from  an  induction  coil  or  similar  source,  is 
called  the  "primary  circuit,"  the  other  being  called  the  "secondary 
circuit." 

a.  Magnetic  or  Inductive  Coupling. — In  this  case  the  mutual  action 
of  the  two  systems  is  procured  only  through  their  magnetic  field :  mutual 
induction*  of  the  two  circuits.  Fig.  110  illustrates  a  case  of  this  kind 


FIG.  110. 

for  two  condenser  circuits;  the  bracket  between  the  two  coils  SS  is  in- 
tended to  indicate,  here  and  in  following  diagrams,  that  the  coils  are 
mutually  inductive. 

b.  Galvanic  or  Conductive  Coupling. — In  Fig.  Ill,  which  shows  a  case 
of  this  kind,  the  parts  drawn  in  heavy  lines  may  be  considered  as  con- 
stituting the  primary  circuit,  while  the  fainter  lines  together  with  the 
coil  S  form  the  secondary  system;  the  coil  S  is  therefore  common  to 
both  circuits.  The  arrangement  of  Fig.  Ill  may  be  conceived  as  having 
been  developed  from  that  of  Fig.  110  by  first  winding  the  two  coils 
S  of  Fig.  110  next  to  each  other  on  a  common  core,  as  illustrated  by 
the  coils  Si  and  $2  of  Fig.  112,  and  finally  superimposing  them  until 
they  become  a  single  winding.  It  is  evident  that  in  this  case  there  is  a 
magnetic  coupling  of  the  two  circuits  just  as  there  is  in  Fig.  110 — the 

*  For  the  electromotive  forces  En  and  En  induced  in  /  by  the  secondary  circuit 
and  in  //  by  the  primary  circuit,  we  have,  as  is  well-known : 

Eno  =  wLlo  X  /20;  Ei-2<>  =  o>L2i  X  7i0  80 
79 


80  WIRELESS  TELEGRAPHY 

current  /i  in  the  primary  circuit  produces  a  magnetic  flux  in  the  coil  S, 
which  flux  in  turn  induces  an  EMF  in  the  secondary  circuit  which  also 
contains  S. 

However  to  the  magnetic  coupling  there  is  here  added  another  kind 
of  coupling.  Even  if  S  in  Fig.  Ill  were  a  non-inductive  (e.g.,  electrolytic) 
resistance  and  both  circuits  were  so  arranged  that  absolutely  none  of  the 
magnetic  lines  of  force  of  one  could  pass  through  the  other  (that  is  their 
mutual  inductance  were  zero),  there  would  nevertheless  exist  a  coupling 
of  the  two  circuits.  The  current  in  the  primary  circuit  would  cause  a 
difference  of  potential  between  the  ends  of  S  which  would  in  turn  cause  a 
current  to  flow  in  the  secondary  circuit.  This  kind  of  coupling  is  called 
"galvanic"  or  "conductive." 

Fig.  Ill  therefore  illustrates  a  combination  of  magnetic  and  galvanic 
coupling,  which  is  frequently  referred  to  as  "direct  coupling."81 


FIG.  111.  FIG.  112. 

In  this  case  to  the  electromotive  forces  EH  and  E&  produced  in  the 
primary  and  secondary  circuits  by  their  magnetic  coupling  there  are 
added  the  electromotive  forces  Egi  and  Eg2  caused  by  their  galvanic 
coupling,  the  various  values  being:81 

Eglo  =  Rho;  Eilo  =  <»L  X  I*o 

Eg2°o  =  RI^  Ei2o  =  coL  X  7i§ 

(R  and  L  are  the  effective  resistance  and  coefficient  of  self-induction  of 
the  coil  S  in  Fig.  111).     It  follows  that 


_  __ 

Egi0       Eg20        R 

i.e.,  the  ratio  of  the  amplitudes  of  the  electromotive  forces  due  to  magnetic 
coupling  to  those  due  to  galvanic  coupling  is  equal  to  the  ratio  of  the 
inductance  of  the  coil  S  to  its  resistance.  However,  according  to  Art. 
41a,  the  inductance  of  wire  circuits  (such  as  are  generally  used  in  radio- 
telegraphy),  if  not  made  of  extremely  thin  or  very  poorly  conducting 
wires,  is  usually  much  greater  than  the  resistance. 

Hence  in  all  practical  cases  of  importance  involving  a  combined 
magnetic  and  galvanic  (direct)  coupling,  the  effect  of  the  magnetic  coup- 
ling only  need  be  considered.  The  connections  shown  in  Fig.  Ill  niay 
therefore  be  considered  as  practically  identical  with  those  of  Fig.  110.81 


COUPLED  CIRCUITS 


81 


c.  Electric  or  Capacity  Coupling.— The  mutual  effect  of  the  two  condenser 
circuits  in  Fig.  113  is  brought  about  by  the  electric  field  between  the  con- 
denser plates.  As  soon  as  an  electric  field  exists  between  the  plates  of  Ci, 
a  difference  of  potential  is  produced  between  the  plates  of  (72.  Oscilla- 
tions in  the  primary  circuit  therefore  necessarily  cause  oscillations  in  the 
secondary. 


FIG.  113. 

Variations  of  the  arrangement  of  Fig.  113  are  shown  in  Figs.  114  and 
115,  which  also  have  electric  coupling.  Here,  as  in  all  practical  cases, 
the  electrical  coupling  consists  in  having  one  (Fig.  115)  or  several  (Fig. 
114)  condensers  common  to  both  circuits  ("capacity"  coupling). 

53.  Loose  and  Close  Coupling. — a.  Any  coupling  between  two 
circuits  involves  not  only  an  action  or  effect 
of  the  primary  upon  the  secondary,  but  also 
a  reaction  of  the  secondary  upon  the  primary 
circuit.  If  the  reaction  is  so  slight  as  to  have 
very  little  effect  upon  the  oscillations  in  the 
primary  circuit,  the  coupling  is  said  to  be 


To  Induction  Coil 


FIG.  114. 


FIG.  115. 


"loose,"  or  if  the  reaction  is  not  noticeable  the  coupling  is  said  to  be 
"extremely  loose."  If  the  reaction  is  very  marked,  we  speak  of  a 
"close  coupling."  A  magnetic  coupling  becomes  looser,  the  farther 
apart  the  two  circuits  are  brought,  other  things  remaining  equal;  a  com- 
bined magnetic  and  galvanic  (direct)  coupling  becomes  looser,  the  more 
the  portion  common  to  the  two  circuits  is  reduced. 


82 


WIRELESS  TELEGRAPHY 


gives  a  measure 


b.  To  a  certain  extent*  the  "Coefficient  of  Coupling' 
of  the  extent  of  a  magnetic  coupling. 

If  both  primary  and  secondary  circuit  have  quasi-stationary  current 
(two  condenser  circuits  or  one  condenser  circuit  and  one  open  oscillator, 
in  which  the  current  amplitude  is  practically  the  same  throughout),  then 
the  coefficient  of  coupling 


Lsl2 


xLt 


in  which  the  coefficient  of  mutual  induction  Lsi2  (or  Ls2l)  has  practically 
the  same  value  as  for  slowly  changing  currents. 

If  the  current  amplitude  varies  along  different  points  of  one  of  the 
circuits,  then 

Lt, 


A' 


I 

v 


4 


Here  LI  and  L2  are  the  respective  effective  coefficients  of  self-induction 
and  Li2  and  L2l  are  respectively  the  "effective  coefficients  of  mutual 
induction."  The  value  of  the  latter  depends  on 
the  distribution  of  the  current  and  on  the  point 
or  portion  at  which  the  circuits  are  coupled,  f 
The  difference  between  Li2  or  L2l  and  Lsi2  or 
LsZi  (for  quasi-stationary  currents)  becomes  less 
as  the  point  of  coupling  comes  nearer  to  the 

current  anti-node  and  as  the 

current  distribution  becomes 

more  even. 

54.  Methods  of  Coupling.52 

— a.  Direct  coupling  is  usually 
•    obtained    by  tapping  off  the 

secondary  from  a  portion  CD 

(Fig.  116)  of  a  coil  AB  in  the 

primary  circuit  or  vice  versa. 

If  either  or  both  the  taps  at 
C  and  D  are  clips  or  sliding  contacts,  the  coefficient  of  coupling  can  be 
varied  in  steps  or  continuously. 

b.  For  magnetic  coupling,  the  well-known  "Tesla  transformer, " 
consisting  of  two  concentric  cylindrical  coils  (Fig.  117)  was  formerly 
in  general  use.  If  one  of  the  coils  is  movable  (the  outer  coil  in  Fig.  117) 

*  See  foot-note  to  Art.  68a. 

f  If  the  current  distribution  in  one  of  the  circuits  is  sinusoidal  [Art.  18] 

2irX  , 


FIG.  117. 


in  which  x  is  the  distance  of  the  point  of  coupling  from  the  current  anti-node  and  X 
the  wave-length  of  the  oscillations. 


COUPLED  CIRCUITS 


83 


a  continuous  variation  of  the  coefficient  of  coupling  may  be  obtained. 
Two  flat  coils,  movable  toward  or  from  each  other,  form  another  coup- 
ling arrangement,  convenient  for  the  laboratory. 


FIG. 


More  recently,  arrangements  in  which  one  of  the  coils  can  be  turned 
or  rotated  have  been  preferred.     All  forms  of  variometer  [Art.  38c]  can 


FIG. 


serve  as  such  coupling  devices  by  connecting  one  coil  into  the  primary, 
the    other    into    the    secondary    circuit.     A    widely    used    construction 


84 


WIRELESS  TELEGRAPHY 


(Telefunken)  is  shown  in  Fig.  118.  The  upper  coil  in  the  device  shown 
in  Fig.  119  (C.  LORENZ)  can  be  turned  and  displaced  sideways  at  the 
same  time. 

2.  LOOSE  COUPLING  OF  DAMPED  OSCILLATING  CIRCUITS 

55.  Coupling  of  Oscillator  to  Closed  Circuit. — a.  Assume  an  oscillator, 
e.g.,  the  condenser  circuit  7,  Fig.  120,  to  be  very  loosely  coupled  to  a 
closed  circuit  (77,  Fig.  120).  Oscillations  in  the  condenser  circuit 
immediately  induce  oscillations  of  the  same  frequency  and  the  same 
damping  in  the  closed  circuit.  The  amplitude  of  the  current  in  the 
closed  circuit,  however,  instead  of  immediately  starting  at  its  maximum 
value  must  first  rise  up  to  its  maximum,  as  shown  for  a  particular 
case  in  Fig.  121.* 


To  Induction  Coil 


FIG.  120. 


FIG.  121. 


6.  The  arrangement  of  Fig.  120  finds  frequent  application  in  practice 
for  the  connection  of  a  measuring  instrument  in  the  closed  circuit,  in- 
stead of  placing  it  directly  in  the  oscillator.  The  requirements  for  cor- 
rect indication  in  such  measurements  are: 

1.  Q,  the  heat  developed  in  the  instrument  must  be  proportional  to 
Q',  the  heat  which  would  be  developed  in  the  same  instrument  if  the 
latter  were  connected  in  the  oscillator  itself,  i.e., 


2.  The  factor  A  must  be  independent  of  the  frequency.! 

R 

*  Mathematically  expressed  the  current  induced  in  the  closed  circuit  72  =  h0e~  L 
(t  =  time,  R  =  resistance  and  L  =  coeff.  of  self-induction  of  the  closed  circuit). 

t  The  second  condition  is  eliminated  if  the  arrangement  is  used  for  measure- 
ments at  a  single  frequency. 


COUPLED  CIRCUITS 


85 


Both  conditions  are  fulfilled,  though  at  the  expense  of  the  current 
amplitude,  if  the  inductance  of  the  closed 
circuit  is  made  very  large  as  compared 
to  the  resistance. 

c.  If  the  coupling  is  loose,  but  not 
extremely  loose,  so  that  there  is  a  slight 
but  appreciable  reaction  upon  the  os- 
cillator, we  are  justified  in  concluding 
that  the  reaction  causes  an  apparent 
reduction  of  the  self-induction  and  an 
apparent  increase  of  the  resistance  in 
the  oscillator.  According  to  Art.  3  and 
8d,  this  results  in  increased  frequency 
and  decrement. 

For  some  purposes  it  is  convenient 
to  substitute  an  "equivalent  resistance" 
R,  for  the  closed  circuit,  under  the  con- 
dition that  RI2eff  (I  =  current  in  the 
oscillator)  is  equal  to  the  energy  trans- 
ferred from  the  oscillator  to  the  closed 
circuit  per  second.  R  increases  as  the 
coupling  is  made  closer  in  the  proportion 

56.  Extremely  Loose  Coupling  of  Two 
Oscillators  (V.  BjERKNES84). — a.  In  our 
conception  of  very  loose  coupling,  the 
oscillations  in  the  primary  circuit  remain 
practically  unaffected  by  the  coupling 
with  the  secondary  circuit.  In  the  sec- 
ondary there  are  produced  in  general, 
two  distinct  oscillations: 

1.  One    having   the  same  frequency 
and  damping  as  the  oscillation  of  the 
primary — the  so-called  "forced"  or  "im- 
pressed oscillation." 

2.  The  other  having  the  character- 
istic frequency  and  damping  of  the  sec- 
ondary circuit — the  "free"  or  "natural 
oscillation." 

b.  The  amplitudes  of  both  the  forced 

and  natural  oscillations  become  a  maxi-       „  s-  S-  3-  a-  «  s-  S-  s-  s-  T- 
mum  when  the  natural  frequency  of  both 

primary  and  secondary  circuits  is  the  same,  i.e.,  when  the  two  circuits 
are  "tuned"  or  "in  resonance."     Then  the  forced  and  natural  oscilla- 


86 


WIRELESS  TELEGRAPHY 


tions  have  the  same  frequency  and  may  be  considered  as  constituting 
a  single  oscillation. 

The  amplitude  curve  of  this  single  oscillation,  assuming  that  that  of  the 
primary  circuit  is  an  exponential  curve,  is  determined  as  follows.  First 
the  amplitude  curve  of  the  forced  oscillation  (with  the  decrement  d\) 
of  the  primary  circuit  (e.g.,  the  dash  and  dot  exponential  curve  in  Fig. 
122)  is  plotted,  then  the  amplitude  curve  of  the  natural  oscillation  (with 
the  decrement  d2)  of  the  secondary  circuit  (e.g.,  the  full-line  curve  in 
Fig.  122)  is  plotted,  starting  the  latter  with  the  same  initial  amplitude 
as  the  former.  Then  the  difference  of  these  two  curves  (dashed  line  in 
Fig.  122)  is  the  amplitude  curve  of  the  resultant  oscillation.85 

In  Fig.  122  di  =  0.08  and  d2  =  0.02,  while  in  Fig.  123  di  =  0.08  and 
d2  =  0.2.  The  former  corresponds  roughly  to  the  coupling  of  a  con- 
denser circuit  with  spark  gap  to  a  condenser  circuit  without  spark  gap  but 
containing  a  measuring  instrument  of  moderate  sensitiveness.  The  other 
case  corresponds  approximately  to  the  coupling  of  a  condenser  circuit 
with  spark  gap85  to  a  straight  lineal  oscillator. 


FIG.  123 


If  the  decrements  of  the  two  oscillations  are  widely  different,  the  ampli- 
tude curve  of  the  resultant  oscillations  quickly  tends  to  become  identical 
with  that  of  the  oscillation  having  the  lower  damping;  the  result,  in 
short,  is  much  the  same  as  if  the  weakly  damped  oscillation  alone  existed. 
It  follows  that: 

1.  In  case  the  primary  has  a  much  lower  decrement  than  the  second- 
ary circuit,  the  oscillations  obtained  in  the  secondary  will  be  practically 
as  slightly  damped  as  those  in  the  primary. 

2.  In  case  the  primary  has  a  much  higher  decrement  than  the  second- 
ary circuit,  the  oscillations  obtained  in  the  latter  are  as  slightly  damped  as 
if  only  the  slightly  damped  natural  oscillations  of  the  secondary  were 
present.     The  primary  circuit  simply  serves  to  excite  or  set  into  motion 
the  natural  oscillations  of  the  secondary. 

c.  From  the  construction  of  the  amplitude  curve  given  in  b,  it  follows 
that  the  highest  value  which  the  amplitude  of  the  resultant  oscillation 
can  in  any  case  assume,  the  so-called  "maximum  amplitude"  (Imax), 


COUPLED  CIRCUITS  87 

can  never  be  greater  than  the  amplitude  70  of  the  impressed  oscillation. 
For  the  latter  with  two  circuits  having  quasi-stationary*  currents,85  we 
have: 


T 

" 


and  for  the  maximum  amplitude: 


57.  Loose  Coupling  of  Two  Oscillators  (M.  WiEN).86 — If  the  coupling 
is  not  extremely  loose,  yet  sufficiently  loose  to  make  K2  <  f-^= — - j  > 

a  slight  reaction  becomes  noticeable.  Consequently  there  is  a  change 
in  the  damping  of  the  two  oscillations.  The  decrement  of  the  more 
weakly  damped  oscillation  is  increased  and  that  of  the  more  highly 
damped  oscillation  is  reduced,  that  is  the  two  decrements  come  nearer 
to  each  other  in  value. 

The  following  are  the  equations  for  the  new  decrements  d1  and  dIT 
with  primary  circuits  having  no  spark  gap: 


-2W 

f       1 
z  > 

\-dz 


ty  V*X     i     *"* 

or,  as  long  as  K  is  small  as  compared  to 

ZTT 

d1  =  di  +  ~ — T- 

«2  —  «1 

d"  -  d,  -  /^- 

«2    —  «1 

3.  CLOSE  COUPLING  OF  TUNED,  DAMPED  OSCILLATING  CIRCUITS 

58.  Form  of  the  Oscillations. — Assume  two  tuned  oscillators,  say  two 
condenser  circuits,  which  before  coupling  had  the  frequency  N  and  wave- 
length X  and  the  respective  decrements  di  and  dz,  to  be  coupled.  The 
coupling  is  not  made  loose,  so  that  in  any  case 

-d2\2t 


*  For  currents  not  quasi-stationary  L  S2]l  should  be  replaced  by  L2l  in  the  equations 
for  70  and  I  max,  which  latter  are  to  be  understood  as  values  at  the  current  anti-nodes. 

t  In  the  very  unfavorable  case  of  di  =  0.08,  d2  =0.2,  K  must  >  0.02  to  meet 
this  condition;  for  K  >  0.1,  K'  becomes  practically  identical  with  K  in  all  cases 
encountered  in  actual  practice. 


88 
whence 


WIRELESS  TELEGRAPHY 


Whenever  the  coupling  is  fairly  close,  K2  is  considerably  greater  than 
n  —  -)  '  so  that  the  quantity  Kf  is  not  much  different  from  the  coup- 

ling coefficient  K.  (See  note  f;  P-  87.) 

Under  these  conditions  there  are  in  general87  two  distinct  oscillations 
the  so-called  "coupling  oscillations"  ("coupling  waves")  produced 
in  both  the  primary  and  the  secondary  circuit,  having  two  distinct  frequencies, 
N1  and  N11,  and  two  distinct  decrements,  d1  and  d11. 

If,  as  heretofore,  we  use  7i  and  Vi  to  indicate  current  and  voltage  in 
the  primary  circuit,  72  and  V2  the  same  in  the  secondary  then  7i  (and  Vi) 
as  well  as  72  (and  V2)  are  the  results  of  two  oscillations.  Hence  we  may 
write  : 

7    =  I  T  +  I  u     \ 

y1  =  y  T       y  jj     for  the  primary  circuit. 


I 

2 
Vz 


4-  I 
* 

~r  V  2 


for  the  secondary  circuit. 


The  various  oscillations  have  the  following   frequencies,  wave-lengths 
and  decrements. 


(and  F2J) 


59.  The  Frequency  of  Coupling  Waves.  —  a.  Primary  Circuit  without 
Spark  Gap.  —  Let  the  index  7  refer  to  the  oscillation  having  the  higher 
frequency  and  shorter  wave-length.  Then  we  have: 


n  N 

" 


_ 
N" 


_ 

jl  +  K' 
'-"  Vl^K'' 


and 


£ 


,n 


(2) 


Hence,  the  greater  Kf,  i.e.,  the  closer  the  coupling,  the  more  will  the 
frequencies  (wave-lengths)  of  the  coupling  waves  differ  from  each  other  and 
from  the  original  common  frequency  (wave-length) . 

b.  Primary  Circuit  with  Spark  Gap. — In  this  case  also  the  relations 
between  the  frequencies  before  and  after  coupling  are  of  the  form  of  equa- 
tions (1).  It  is  not  definitely  known,  however,  though  this  is  of  no  prac- 


COUPLED  CIRCUITS 


89 


tical  importance,  whether  the  factor  K'  has  the  relation  to  the  coefficient 
of  coupling,  K,  and  the  decrements  given  by  equation  (1)  of  Art.  58. 
The  quantity  which  actually  determines  the  extent  of  the  coupling  and 
which  may  be  directly  measured  by  test  [Art.  87]  is  the  factor  K'  for  cir- 
cuits with  spark  gap  also. 

K'  is  called  the  "degree  of  coupling."  Its  value  is  frequently  ex- 
pressed in  percentage,  thus:  "3  per  cent,  coupling"  means  Kr  =  0.03. 
The  relation  between  N1,  N11  and  N,  as  well  as  XJ,  XIJ  and  X  is  given  in 
Table  X  for  different  values  of  K'. 

c.  The  resultant  oscillation  produced  from  the  two  coupling  oscilla- 
tions of  different  frequency  is  of  the  form  shown  diagrammatically  in 

Fig.  130,  and  shown  in  Fig.  124  as  ob- 
tained with  an  oscillograph  (H.  DIESSEL- 
HORST88)  and  in  Fig.  125  as  photo- 
graphed from  the  spark  discharges  (H. 
RAU88).  The  resultant  oscillation  may 
be  conceived  as  having  the  frequency 
N  and  an  amplitude  which  periodically 
increases  and  decreases,  similarly  to  the 
beats  or  pulsations  of  a  tone  which  are 
observed  in  acoustics. 


1! 


• 

fi  « 


!••  II 


I'l 


FIG.  124. 


FIG.  125. 


The  greater  the  difference  between  the  frequencies  of  the  two  os- 
cillations, i.e.,  the  closer  the  coupling,  the  greater  is  the  number  of  pul- 
sations obtained  per  second.  This  number,  S,  which  is  the  number  of 
times  per  second  that  the  amplitude  passes  through  zero,  is  given  by 

S  =  N1  -  N11  =  approx.  NK' 
Hence  the  duration  of  one  beat  or  pulsation  is  approximately  =vr^; 

seconds  =  -^  periods. 

d.  The  energy  relations,  as  is  evident  from  Fig.  130,  are  as  follows: 
Originally  the  entire  energy  resides  in  the  primary  circuit.  After  half 
of  one  pulsation  the  amplitude  of  the  oscillation  in  the  primary  circuit  is 


90 


WIRELESS  TELEGRAPHY 


zero,  while  that  in  the  secondary  is  a  maximum  and  the  entire  energy  has 
been  transferred  to  the  secondary  circuit.  After  another  half  pulsation 
all  the  energy  is  again  back  in  the  primary  and  the  secondary  is  at  zero, 
etc.,  etc.  In  short,  the  energy  continues  to  swing  back  and  forth  be- 
tween the  primary  and  secondary  circuits. 

60.  The  Decrements  of  the  Coupling  Waves. — a.  Primary  Circuits 
without  Spark  Gap  (P.  DRUDE89). — The  relations  of  the  decrements  be- 
fore and  after  coupling  are  expressed  by: 

+  d2    N^_   _  dd-f 
2       '  N   :          2 


d1  = 


ill 


d"  = 


d, 


N 


J^ 
X' 
_V 
X" 


d1 

d11 


N1 
Nn 


X' 


So  that  while  for  low  degrees  of  coupling  the  decrements  of  the  two 
oscillations  are  approximately  equal  to  the  average  value  of  the  decre- 


0.25 


0.20 


0.15 


0.10 


0.05 


=$=ZT 


Theor. 


dlj-  Thcorr 


t 


0  0.1 

K'  — 


0.2 


0.3 


FIG.  126. 


0.4 


0.5 


ment  before  coupling,  as  the  coupling  becomes  closer,  the  decrement  of  the 
oscillation  having  the  shorter  wave-length  increases  and  that  of  the  oscillation 
having  the  longer  wave  becomes  less  than  the  average  value  mentioned  above. 
Theoretically  the  closest  possible  coupling  exists  when  K'  =  1;  in 
practice  about  the  highest  value  obtainable  is  approximately  K'  =  06. 
For  this  latter  value,  we  have: 

N1  =  1.6  N  d1  =  0.8  (di  +  d2) 


=  0.8  N 


d11  =  0.4  (dd  +  d2) 


Hence  in  practice  the  frequency  and  decrement  of  the  oscillation  of 
shorter  wave-length  will  at  most  be  twice  what  they  are  for  that  of  the 
longer  wave. 


COUPLED  CIRCUITS 


91 


b.  Primary  Circuit  with  Spark  Gap. — (C.  FiscHER90). — In  this  case 
the  relations  of  a  do  not  hold. 

1.  The  decrements  of  both  oscillations,  particularly  if  the  coupling 
is  loose,  are  greater  than  would  follow  from  a. 

2.  It  is  by  no  means  always  the  oscillation  of  shorter  wave-length 
which  is  the  most  highly  damped.     On  the  contrary,  this  usually  is  more 
slightly  damped  than  the  oscillation  of  greater  wave-length. 

The  conditions  obtained  by  coupling  a  condenser  circuit  containing 
a  spark  gap  with  another  having  no  gap,  were  observed  by  C.  FISCHER, 
whose  results  are  shown  in  Figs.  126  and  127.  Fig.  126  refers  to  the 
case  of  primary  and  secondary  capacities  being  practically  equal*  while 


0.25 


0.20 


0.15 


0.10 


0.05 


in  Fig.   127 f  the  capacity  in  the  primary  circuit  is  much  greater  than 
that  in  the  secondary. 

61.  Amplitude  and  Phase  of  the  Oscillations.91 — a.  Amplitude.^ — 
The  current  amplitudes  of  the  individual  oscillati'ons  have  the  same  re- 
lation, approximately,  as  their  frequencies,  i.e., 


III 

r1n       /»„     N 


II 


_2  o   _ 
II    ~         II  ~        II    ~         I 

/,„       /2,     A          X 

*  Ci  =  C2  =  0.85  X  10-3  MF.  Li  =  L2  =  approx.  22,000  C.<?.£  Length  of 
gap  =  6  mm. 

t  Ci  =  5.29  X  10~3  MF.  L:  =  6230  C.G.S.  Gap  =  6.8  mm.  approx.  C2  = 
0.45  X  10-3  MF.  L,  =  73,000  C.G.S. 

|  If  the  current  in  one  of  the  circuits  is  not  quasi-stationary,  the  current  amplitude 
is  to  be  understood  as  the  value  at  the  current  anti-node. 


92  WIRELESS  TELEGRAPHY 

The  current  amplitude  of  the  oscillation  having  the  shorter  wave-length 
is  therefore  greater  than  that  of  the  longer  wave  oscillation. 

Assume  a  given  known  value  for  the  initial  potential  FIO  of  the  primary 
circuit,  then  we  have  the  following  expressions  for  the  current  and  voltage 
amplitudes  in  a  secondary  circuit  having  quasi-stationary  current:* 


b.  Phase. — If  we  consider  as  positive  the  direction  of  the  oscillating 
current  /  (one)  in  both  circuits,  the  vector  diagram  will  have  the  form  of 
Fig.  128.  The  angles  of  phase  displacement  <p  and  <pn  are  given  approxi- 
mately by 

dt-di  N 


ii  -  d*  ~  di  -A     N 

n  *  27T      '  Kf'  N11 

In  all  practical  cases,  as  long  as  the  coupling  is  fairly  close  f  these 
angles  are  very  small.  We  may  therefore  state  roughly:  of  the  oscilla- 
tions in  the  primary  and  secondary  circuits  having  the  same  frequency,  the 


FIG.  128. 

one  pair  (I^,  and  I*\)  are  almost  in  phase,  while  the  other  pair  (Ii1  and 
727It)  are  approximately  180°  apart. 

c.  The  maximum  amplitude  of  the  resultant  oscillation  in  the  secondary 
circuit  depends  not  only  upon  the  amplitude  of  the  two  component 
oscillations,  but  also  upon  their  phase  and  damping. 

*  If  neither  primary  nor  secondary  circuit  has  quasi-stationary  current,  these 
relations,  to  the  extent  of  their  involving  the  voltage,  hold  only  approximately;  those 
independent  of  FIO  are  correct  if  the  value  of  the  current  anti-node  is  taken  as  the 
current  amplitude. 

f  Assume  d\  =  0.08  and  d2  =  0.2;  then  Kr  need  only  be  large  as  compared  to 
0.02.  If  the  secondary  circuit  is  less  damped  the  conditions  become  still  more 
favorable. 

%  i  is  used  in  Fig.  128  instead  of  the  capital  /. 


COUPLED  CIRCUITS 


93 


If  the  primary  circuit  contains  no  spark-  gap,  we  have,  for  quasi- 
stationary  current  in  the  secondary  (P.  DmiDE89): 


in  which  /  is  a  factor  which  depends  upon  the  sum  of  the  decrements 
previous  to  coupling,  d\  +  dz,  and  upon  the  degree  of  coupling  as  shown 
in  Fig.  129. 

For  primary  circuits  with  a  spark  gap  these  curves  for  /  are  somewhat 
different.     The  difference,  so  far  as  this  question  has  been  investigated 


to  date  (J.  ZENNECK91a,  C.  FiscHER90),  seems  to  consist  mainly  in  that  the 
curves  have  either  a  true  maximum  or  at  least  do  not  increase  beyond  the 
value  reached  between  K'  =  0.2  and  K'  =  0.4. 


4.  QUENCHING  ACTION  IN  COUPLED  CIRCUITS  (M.  WiEN92) 

62.  Form  of  the  Oscillations. — In  Art.  59  it  was  stated  that  under  the 
conditions  therein  specified  the  oscillations  in  the  primary  and  secondary 
circuits  would  be  of  the  nature  illustrated  in  Fig.  130.*  In  the  primary 
circuit,  after  lapse  of  half  a  pulsation,  the  amplitude  of  the  oscillation  is 
zero  or  nearly  zero.  It  then  increases  again,  this  being  due  to  the  fact 
that  the  secondary,  whose  amplitude  is  at  its  maximum  at  that  moment, 
induces  an  EMF  in  the  primary,  producing  a  difference  of  potential 
between  the  electrodes  of  the  spark  gap. 

*  Assumption:  d1  =  d11  =  0.08;  K'  =  0.16. 


94 


WIRELESS  TELEGRAPHY 


The  conditions  may  be  such,  however,  that  the  spark  gap,  during  the 
time  in  which  the  amplitude  in  the  primary  circuit  is  very  small,  becomes 


Secondary  Circuit 

FIG.  130. 


Secondary  Circuit 


FIG.  131, 


o  JH 
"' 


ituAiiiiiiiiiMUiiiiiiiiii1 


FIG.  132. 

so  deionized,  that  the  EMF  induced  by  the  secondary  is  no  longer 
sufficient  to  start  or  " ignite"  a  spark  discharge  across  the  gap.  As  a 
result  the  spark  gap  remains  quenched — whence  the  terms  "quenching 


COUPLED  CIRCUITS  95 

action"  or  "quenched  gap."  The  oscillations  in  the  primary  then 
discontinue  entirely  and  the  secondary  circuit  continues  to  oscillate  with 
its  natural  damping  and  at  its  natural  frequency  just  as  if  the  primary 
circuit  did  not  exist.  (Compare  the  diagrammatic  Fig.  131*  and  the 
spark  photograph  Fig.  132  [H.  RAU88].) 

63.  Various  Types  of  Quenched  Gaps. — a.  Very  short  metallic  spark 
gaps  (M.  WIEN)  are  of  special  importance  in  practice. 

Not  only  the  material  of  which  the  electrodes  are  made  but  also  the 
gas  in  the  gap  between  them  is  of  importance.  Particularly  good  quench- 
ing action  is  obtained  with  silver  and  copper,  aluminium  is  less  satis- 
factory and  zinc,  tin  and  magnesium  do  not  give  good  quenching  (M. 
WiEN92);  platinum-iridium  alloy  is  also  quite  effective  with  short  gap 
lengths  (H.  BoAS93).  The  quenching  action  is  increased  if  the  sparks  are 
passed  through  hydrogen  instead  of  air  (A.  Espinosa  de  los  M  outer  os^)\ 

b.  For  laboratory  purposes  the  so-called  mercury-arc  lamp,  i.e.,  an 
exhausted  glass  tube  with  mercury  electrodes  (R.  RENDAHL95)  is  very  well 
adapted.     Apparently  the  only  essential  element  in  the  form  of  this 
lamp  is  the  provision  of  a  sufficiently  large  space  over  the  electrodes  for 
cooling  and  condensing  the  mercury  vapor.     Moreover  the  tube  must 
have  a  high  vacuum  and  pure  mercury  must  be  used. 

c.  With   primary   circuits   having  long    gaps,  which   in   themselves 
would  have  no  quenching  action,  it  is  possible  to  secure  quenching  by 
greatly  increasing  the  damping  of  the  primary  circuit  through  an  in- 
serted resistance,  or  better  still,  by  inserting  a  glass  tube  filled  with  gas 
at  very  low  pressure  (e.g.,  3  mm.  mercury)  and  having  metallic  electrodes 
— a  so-called  "quenching  tube"  (M.  WiEN92). 

64.  Requirements    for    Good    Quenching. — a.  Time-lapse     of    One 
Pulsation. — In  view  of  the  fact  that  the  primary  circuit  consumes  less 
energy  the  sooner  the  oscillations  in  it  are  quenched,!  i.e.,  for  the  sake  of 
efficiency,  it  is  desirable  to  make  the  coupling  as  close  as  possible.     The 
closer  the  coupling,  the  shorter  will  be  the  time-lapse  or  duration  of  one 
pulsation,  which  is  the  time  during  which  the  primary  circuit  remains 
active  [59c]. 

On  the  other  hand,  however,  the  time  during  which  the  amplitude  in 
the  primary  remains  very  small  and,  hence,  the  time  during  which  the 
spark  gap  is  subjected  to  deionization  becomes  shorter  as  the  coupling 
is  made  closer.  If  this  time  is  made  too  short,  "pure"  quenching  is  no 
longer  obtained,  i.e.,  the  primary  oscillation  is  not  suppressed  after  one- 
half  a  pulsation.  Either  coupling  oscillations  result  or  intermediate 
conditions  between  distinct  coupling  oscillations  and  pure  quenching 

*  Assumption:  dz  =  0.03;  otherwise  just  as  for  Fig.  130. 

t  In  regard  to  hydrogen  quenched  spark  gaps  [see  Art.  109e]. 

t  For  the  same  decrement;  this  also  affects  the  efficiency  [6]. 


96  WIRELESS  TELEGRAPHY 

are  obtained;  thus  the  primary  oscillations  disappear  only  after  one 
and  one-half  or  two  and  one-half  pulsations  (Fig.  133,  H.  RAU88). 

Hence  close  coupling  is  desirable  for  efficiency,  while  loose950  coupling 
is  needed  for  pure  quenching.  It  follows  that  for  every  spark  gap  there 
must  exist  a  "critical  degree  of  coupling,"  at  which  pure  quenching  is 
still  just  obtainable.  This  is  of  course  always  used  in  order  to  secure 
as  high  efficiency  as  possible.  The  higher  the  critical  percentage  of  coup- 
ling, the  better  will  be  the  quenching  action  of  the  given  spark  gap. 

b.  Pureness  of  the  Pulsations. — It  is  most  favorable  for  the  quenching 
action  if  the  amplitude  of  the  resultant  oscillation  in  the  primary  circuit 
really  becomes  zero  after  the  first  half  pulsation,  that  is,  if  the  pulsa- 
tions are  pure.  The  essential  condition  for  this,  however,  is  that  both 
oscillations,  after  half  a  pulsation,  have  the  same  amplitude  but  are 
opposite  in  phase. 

Whether  this  condition  obtains  depends  upon  the  accuracy  of  the 
tuning  between  the  primary  and  secondary  circuits;  the  more  exact 
the  tuning,  the  purer  will  be  the  pulsations,  other  things  being  equal. 


Primary 
circuit 


Secondary 
circuit 


FIG.  133. 


Moreover,  even  with  perfect  tuning,  it  is  evident  that  the  pureness  of 
the  pulsations  depends  upon  the  initial  amplitude  of  the  two  oscillations 
and  their  decrements.  In  this  connection,  therefore,  the  decrement  of 
the  primary  and  secondary  circuits  becomes  of  importance.  As  the 
decrements  of  the  coupling  oscillations  also  depend  on  the  degree  of 
coupling,  the  latter  affects  the  quenching  action  in  this  way  also. 

Apparently  this  effect  of  the  degree  of  coupling  plays  a  part  in  con- 
nection with  the  following  phenomenon  (H.  RiEGGER7).  If  the  degree 
of  coupling  is  gradually  increased  a  first  critical  coupling  is  reached, 
beyond  which  pure  quenching  is  no  longer  attainable.  If,  however,  we 
proceed  to  make  the  coupling  much  closer,  a  degree  of  coupling' is  reached 
at  which  pure  quenching  is  again  obtained  (second  critical  precentage  of 
coupling) .  In  fact,  under  certain  conditions,  a  third  critical  coupling  may 
occur.  The  critical  degree  of  coupling  of  a  quenched  gap  is  therefore 
by  no  means  always  a  single  definite  quantity. 

The  pureness  of  the  pulsations  probably  also  plays  a  part  in  the 
explanation  of  the  fact  that  by  bringing  the  primary  and  secondary  cir- 


COUPLED  CIRCUITS  97 

cults  slightly  out  of  resonance,  a  pure  quenching  can  be  obtained,  after 
the  quenching  had  been  spoiled  with  primary  and  secondary  entirely  in 
tune  (H.  RiEGGER7). 

c.  The    magnitude    of    the    EMF  induced  in  the  primary  by    the 
secondary  circuit  is  also  affected  by  the  degree  of  coupling;  in  fact,  is 
proportional  to  the   coefficient   of   coupling,   other  things  being  equal. 
Hence  the  greater  the  coefficient,  so  much  greater  is  the  danger  that  a 
discharge  will  pass  across  the  spark  gap  after  half  a  pulsation. 

d.  Lastly,  the  temperature  of  the  electrodes,  that  is,  not  the  average 
temperature,  but  the  maximum  at  any  point  (local  heating]  affects  the 
quenching,    as   when   the   temperature   becomes   very   high   the  gas  is 
highly  ionized,  thereby  greatly  reducing  the  quenching  action  as  well  as 
the  discharge  voltage.     This  makes  it  easier  for  another  spark  to  jump 
across  the  gap  after  the  first  half  pulsation.     Hence,  care  must  be  taken 
that   the  temperature  does  not  rise  too  high  at  any  part  of   the  gap 
electrodes.96 

65.  Concerning  the  Nature  of  the  Quenching  Action. — a.  The  general 
requirement  for  the  best  quenching  action  is  identical  with  the  require- 
ment for  the  quickest  possible  deionization  of  the  spark  gap.  The  de- 
ionization  may  have  several  causes,  viz. : 

1.  The  recombining  of  the  positive  and  negative  ions;  when  two  ions 
of  opposite  charge  collide,  this  may  result  in  a  neutralization  of  their 
charges. 

2.  Diffusion  of  the  ions  from  the  gap  space  between  the  electrodes 
into  space  without;  just  as  a  gas  (e.g.,  illuminating  gas),  pouring  out  from 
some  opening  will  spread  out  in  all  directions  (diffuse)  in  the  surround- 
ing medium  (e.g.,  air),  so  the  ions  diffuse  from  the  space  in  which  they 
were  formed  into  the  surrounding  gas. 

3.  Absorption  of  the  ions  at  the  gap  electrodes.     If  an  ion  comes 
close  to  a  piece  of  metal,  the  latter  will  have  the  same  effect  upon  it  as 
any  uncharged  conductor  has  on  a  charged  body,  viz.,  an  attractive  force. 
Consequently  the  ion  comes  into  contact  with  the  me'tal  and  gives  its 
charge  up  to  it. 

This  last  kind  of  deionization  is  also  influenced  by  the  diffusion  of 
the  ions.  The  faster  new  ions  are  diffused  from  the  outer  space  to  the 
surface  of  the  gap  electrodes,  the  quicker  will  deionization  take  place, 
corresponding  to  a  greater  coefficient  of  diffusion.* 

4.  Deionization  by  the  Electric  Field  between  the  Gap  Electrodes. — If 
an  electric  field  exists  between  the  gap  electrodes,  the  positive  ions  are 
attracted  to  the  negative  electrode,  the  negative  ions  to  the  positive 
electrode,  where  they  give  up  their  charge.     In  the  case  in  point  a  field 

*  The  coefficient  of  diffusion  D  is  defined  as  follows :     If  cr  is  the  concentration 
factor   ( =  change  in  the  number  of  ions  present  in   1   cc.,   along   a  length   of    1 
cm.),  then  the  number  of  ions  diffused  through  a  section   1  cm.  sq.  per  sec.  is  DC'. 
7 


9&  WIRELESS  TELEGRAPHY 

exists  between  the  gap  plates  both  before  and  after  the  moment  at  which 
the  amplitude  of  the  oscillation  in  the  primary  is  zero.  The  field  existing 
after  the  zero  amplitude  is  induced  by  the  oscillations  in  the  secondary 
circuit. 

5.  Deionization  by  Chemical  Changes. — The  conductivity  of  the  gap 
is  due  mainly  to  the  ions  of  the  metallic  vapor  formed  by  the  heating  of 
the  electrodes.     It  is  possible  that  deionization  results  from  a  chemical 
combination  of  the  metallic  vapor  and  the  gas  in  the  gap.     These  changes, 
however,  are  at  present  but  little  understood. 

6.  With  short  metal  spark  gaps  deionization  through  recombination 
and  diffusion  of  the  ions  in  the  outer  space  can  hardly  play  an  important 
part.     This  is  borne  out  by  the  facts  that  the  quenching  action  increases 
very  rapidly  with  decreasing  distance  between  the  electrodes  and  that 
it  is  particularly  good  in  spark  gaps  having  plate  or  disc  electrodes  ar- 
ranged to  make  diffusion  into  the  outer  space  very  difficult. 

Here  then — aside  from  possible  chemical  action — the  deionization 
must  result  mainly  from  the  electric  fielcl  and  absorption. 

If  v  is  the  mean  specific  velocity  of  an  ion,  i.e.,  the  velocity  which  it  obtains  in  an 
electric  field  of  1  volt /cm.,  then  the  velocity,  V,  required  to  move  the  ion  over  a 

d2 
distance  d  between  the  electrode  in  one-half  a  period  = 2N.     Hence,  V  being 

proportional  to  the  square  of  d,  would  be  only  one-hundredth  in  value  for  d  =  0.1 
mm.,  what  it  would  be  for  d  =  1  mm.  Taking  the  normal  value  of  ^  at  atmospheric 
pressure  as  1.5  cm. /sec.,  taking  0.1  mm.  as  the  distance  between  the  electrodes  (gap 
length)  and  the  frequency  N  =  3  X  105/sec.,  which  corresponds  to  a  wave-length 
of  1000  meters,  V  is  found  to  be  40  volts;  for  a  wave-length  of  3000  m.,  V  is  only 
13  volts.  Hence  under  these  conditions  very  low  voltages  suffice  to  produce  complete 
deionization  within  one-half  a  period. 

Similarly  the  time  required  to  reduce  the  number  of  ions  between  the  electrodes 
to  a  given  fraction  of  the  original  number  is  reduced  as  the  gap  length  is  decreased.* 

From  the  foregoing,  it  is  easily  comprehensible  that  the  quenching 
action  of  gaps  increases  very  rapidly  as  the  gap  length  decreases,  and  that 
series  spark  gaps  [Art.  12]  have  a  decided  advantage  in  this  respect  over 
a  single  gap  of  the  same  initial  voltage  (A.  Espenosa  de  los  Monteros9*) : 
a  series  gap  of  ten  units  each  0.1  mm.  long  must  be  much  more  effective 
than  a  single  gap  1  mm.  long.  Presumably,  this  deionization  by  means  of 
the  electric  field  of  the  discharge,  perhaps  also  in  conjunction  with  the 
absorption,  is  the  cause  of  the  very  high  spark  decrement  [Art.  lid] 
characteristic  of  metallic  spark  gaps  and  explains  the  ease97  with  which 
the  oscillations  are  abruptly  discontinued  in  such  gaps  [Art.  9d]. 

c.  The  effectiveness  of  hydrogen  as  the  gap  medium,  and  also  of  gases 
under  low  pressure  (quenching  tubes)  may  be  explained  on  the  assumption 
that  either  diffusion  or  deionization  by  the  electric  field  is  the  principal 

*  This  time  <*d  or  &d2  (d  =  gap  length)  in  accordance  with  original  distribution 
assumed  for  the  ions. 


COUPLED  CIRCUITS 


99 


cause.  The  coefficient  of  diffusion  for  hydrogen  is  about  four  times 
that  for  air  under  the  same  conditions;  furthermore,  it  is  inversely  pro- 
portional to  the  pressure.  However,  very  much  the  same  is  true  of  the 
specific  velocity  of  the  ions.  * 

5.  THE  COUPLING  OF  UNDAMPED  OSCILLATING  CIRCUITS 

66.  Coupling  with  a  Closed  Circuit. — In  a  closed  circuit  coupled 
loosely  to  a  circuit  with  undamped  oscillations,  there  will  also  be  obtained 
undamped  oscillations.  Immediately  upon  starting,  however,  the  same 
complications  described  for  damped  oscillations  [Art.  55]  arise. 

But  in  contrast  to  the  conditions  holding  for  damped  oscillations,  the 
indications  of  a  measuring  instrument  connected  into  the  closed  circuit 


FIG.  134. 


will  not  be  affected  by  these  complications  when  the  oscillations  are 
undamped.  It  is  assumed  that  the  oscillations  are  sinusoidal  and  that 
the  heat,  Q,  developed  in  the  instrument  is  always  proportional  to  the 
heat,  Q',  which  would  be  developed  in  the  same  instrument  if  it  were 
connected  directly  into  the  primary  circuit.  That  is 

Q  =  AQ'  always. 

Here,  just  as  for  damped  oscillations,  the  inductance  of  the  closed 
circuit  must  be  large  in  comparison  to  its  resistance  to  make  the  pro- 
portionality factor  A  independent  of  the  frequency. 

*  The  good  heat  conductivity  of  hydrogen  probably  comes  into  secondary  con- 
sideration only,  in  that  it  causes  a  more  rapid  cooling  of  the  gap  electrodes  and  the 
metallic  vapors. 


100 


WIRELESS  TELEGRAPHY 


damped    natural 
of    the  secondary 


67.  Loose  Coupling  with  an  Oscillator. — a.  As  with  damped  oscilla- 
tions [Art.  56]  two  oscillations  are  obtained  in  the  secondary  circuit,  viz.: 

1.  A  forced  or  impressed 
oscillation    of  the   same   fre- 
quency as  the  primary. 

2.  The 
oscillation 
circuit. 

b.  The  amplitudes  of  both 
oscillations  are  a  maximum 
when  the  secondary  is  in  reso- 
nance with  the  primary  circuit. 
Then  both  oscillations  may  be 
considered  as  a  single  result- 
ant oscillation. 

What  was  stated  in  regard 
to  the  amplitude  curve  for 
damped  oscillations  [Art.  566] 
holds  equally  well  here;  the 
relations,  however,  are  now 
somewhat  simpler  as  the  am- 
plitude curve  of  the  impressed 
oscillation  is  a  straight  line. 
The  construction  is  shown  for 
a  given  case,  Fig.  134,*  the  os- 
cillation curves  being  drawn 
out  in  Fig.  135.* 

As  may  be  seen  from  these 
curves,  the  amplitude  in  the 
secondary  first  increases  grad- 
ually from  zero.  The  time 
required  for  this  increase  up 
to  the  final  maximum  value 
is  the  time  required  for  the 
natural  oscillation  to  die  out, 
hence  is  longer  for  low  than 
for  high  damping.  But  the 
less  the  damping,  so  much 
greater  will  be  the  final  value 
of  the  amplitude,  the  latter 

being  inversely  proportional  to  the  decrement.     This  final  current  ampli- 
tude after  the  natural  oscillation  has  disappeared  has  the  following  value : 

*  Impressed  oscillation :  thin  full  line,  natural  oscillation :  dot  and  dash  line, 
resultant  oscillation :  heavy  full  line. 


COUPLED  CIRCUIT^ ''   A  101 

/9    =wt°    =  o)LS2i-  77-  /io  =  TT"1  '  T~  '   An        (See  foot-note  to  Art.  52«.) 

£12.  -tt2  Li2  0,2 

Fig.  136  shows  the  curve  for  a  decrement  of  0.8  under  the  same  condi- 
tions and  on  the  same  scale  as  Fig.  135  in  which,  however,  the  decrement 
is  0.2.  The  impressed  oscillation  is  in  phase  with  Ea. 

c.  The  final  amplitude  reached  by  the  oscillation  in  the  secondary 
circuit  is  much  greater  than  it  would  be  if  the  secondary  and  primary 
circuits  were  not  in  resonance  or  if  the  secondary  were  a  closed  circuit. 
This  is  explained  as  follows:  With  loose  coupling  only  very  little  energy 
is  transferred  from  the  primary  to  the  secondary  during  each  period  or 
cycle.     But  only  a  part  of  this  energy  is  dissipated  in  the  secondary, 
the  rest  being  stored  by  it.     Consequently  the  energy  accumulated  in 
the  secondary  circuit  grows  with  each 
period.     This  continues  until,  due  to 
the  increasing  amplitude,  the  energy 
loss  in  the  secondary  has  become  equal 
to  the  energy  supplied  by  the  primary 
circuit.     This   point  is  reached  more 
quickly,  the  greater  the  energy  con- 
sumption in  the  secondary  circuit  is  in 
comparison  to  energy  supplied,  i.e.  [Art.  Sd\  the  greater  the  decrement  is. 

68.  Close  Coupling  with  an  Oscillator. — It  is  very  difficult  to  draw 
any  general  conclusions  in  this  connection  with  close  coupling.  For 
undamped  oscillations  can  be  produced  in  a  primary  circuit  only  by 
constantly  replenishing  the  energy  consumed  by  the  oscillations,  and 
the  results  depend  to  a  large  extent  upon  how  this  supply  of  energy  is 
affected  by  the  reaction  of  the  secondary  circuit.^ 

a.  In  the  simplest  case  the  energy  supply  is  such  as  to  maintain  a 
constant  current  amplitude  in  the  primary  circuit.     Then  the  conditions 
in  the  secondary  are  just  the  same  as  with  loose  coupling. { 

This  can  be  secured  by  connecting  the  primary  winding  of  an  in- 
duction coil  to  the  terminals  of  an  alternator  through  a  very  high  series 
resistance,  and  connecting  condensers  to  the  secondary  of  the  induction 
coil;  the  condensers  and  induction  coil  secondary  form  the  secondary 
circuit.  If  the  series  resistance  is  sufficiently  great  in  comparison  to  the 
impedance  of  the  primary  of  the  induction  coil,  then  the  amplitude  of 
the  primary  current,  being  determined  almost  entirely  by  the  series  re- 
sistance, remains  unaffected  by  the  reaction  of  the  secondary  circuit. 

b.  In  the  second  case,  which  is  of  far  greater  importance  in  practice, 

*  Ea  =  EMF  induced  in  the  secondary  by  the  primary  circuit. 

f  In  regard  to  the  arc  method  of  coupling  undamped  oscillations  see  S.  SuBKis970. 

J  Actually  there  is  a  slight  reaction  of  the  secondary  here  too,  even  though  the 
coefficient  of  coupling  may  be  quite  high  under  certain  conditions.  In  such  cases 
the  coefficient  of  coupling  gives  no  correct  measure  of  the  reaction. 


102 


TELEGRAPHY 


the  external  (impressed)  electromotive  force  is  maintained  at  constant 
amplitude  and  frequency.98  These  are  the  conditions  existing,  at  least 
approximately,  when  the  primary  of  a  transformer  or  an  induction  coil 
is  joined  to  the  terminals  of  an  alternator,  driven  by  a  sufficiently  strong 
motor,  while  the  transformer  or  induction  coil  secondary  is  connected 
to  condensers. 

The  initial  increase  of  the  amplitude  is  the  same  qualitatively  as 
with  loose  coupling  [Art.  67]  or  as  in  case  a. 

But  there  is  one  great  difference.  If  the  secondary  frequency  is 
varied  by  changing  the  condensers,  then  the  amplitude  of  the  oscilla- 


0            b             8            12         16           20           24          28  32 

Capacity  in  10~2  M.F. *- 

FIG.  137. 

tions  in  the  secondary  circuit  does  not  become  a  maximum  when  the 
natural  oscillations  of  the  secondary  have  the  same  frequency  as  that  of 
the  primary  circuit.  The  maximum  is  obtained  at  a  secondary  frequency 
which  is  lower  than  that  of  the  primary  and  the  closer  the  coupling,  the 
lower  will  be  the  frequency  at  which  the  maximum  amplitude  of  the 
secondary  oscillations  occurs.*  This  is  due  to  the  simple  fact  that 
the  primary  current  and  hence  also  the  energy  supply  are  by  no  means 
constant,  but  are  much  greater  at  the  lower  frequency  under  the  in- 
fluence of  the  reaction  of  the  secondary  circuit. 

*  Within  certain  limits  we  may  write  for  Nr,  the  frequency  at  which  the  ampli- 
tude is  a  maximum,  approximately 

Nr  =  Ni  Vl  —  K*  (K  =  coefficient  of  coupling) 


COUPLED  CIRCUITS  103 

This  is  shown  by  the  curves  of  Fig.  137,  taken  from  an  article  by  G. 
GLAGE.98  The  values  of  the  capacity  in  the  secondary  circuit  are  plotted 
as  abscissae,  while  the  ordinates  represent  what  is  marked  over  each 
curve.  The  vertical  dot  and  dash  line  indicates  the  capacity  at  which 
the  natural  oscillations  of  the  secondary  have  the  same  frequency  as  the 
primary. 

69.  Difference  between  Damped  and  Undamped  Oscillations.— 
a.  Looking  back  over  the  ground  just  covered  it  appears  that  undamped 
oscillations  are  by  no  means  much  simpler  in  their  various  relations  than 
damped  oscillations.  To  be  sure  an  undamped  oscillation  is  always 
obtained  in  the  secondary  circuit.  But  at  the  start,  exactly  the  same 
complications  arise  as  with  damped  oscillations.  These  complications  are  : 

1.  Secondary  =  a  closed  circuit:  —  a  current  of  the  form  [Art.  55a] 

_Rt 
I  =  I  oe   L    (t  =  time) 

2.  Secondary  =  oscillator:  —  damped  oscillations  [Art.  67  and  68]. 

3.  Secondary  =  circuit  with  capacity  and  self-induction,  but  such 
high  resistance  that  real  oscillations  cannot  take  place  :  —  current  of  the 
form" 


or,  in  case  the  coefficient  of  self-induction  is  very  small 

7  =  IQe~^Rl  10° 

Hence,  considered  from  the  initial  conditions,  the  phenomena  are 
no  simpler  for  undamped  than  for  damped  oscillations. 

6.  For  making  measurements  however  the  conditions  are  quite  different. 
These  disturbances  are  all  of  such  short  duration  that  they  disappear  in 
a  few  seconds  at  the  very  most,  in  fact  within  a  few  thousandths  or  even 
millionths  of  a  second  in  most  practical  cases. 

Hence,  with  undamped  oscillations  these  disturbances  have  long 
disappeared  before  the  instrument  shows  an  appreciable  deflection. 
Only  the  subsequent  undisturbed  oscillations  determine  the  indications 
of  the  instrument. 

With  damped  oscillations,  on  the  other  hand,  the  time  during  which 
these  phenomena  which  we  have  designated  as  disturbances  take  place 
may  be  of  considerable  importance  in  relation  to  the  duration  of  the 
primary  oscillations,  in  fact  they  may  last  even  longer  than  the  latter 
[Art.  5662].  Just  as  often  as  the  primary  oscillations  are  again  set  into 
motion,  so  often  will  these  "  disturbances  "  reappear.  The  heat  developed 
in  a  measuring  instrument  will  therefore  depend  upon  these  disturbances 
as  well  as  upon  the  oscillations  induced  by  the  primary  circuit,  and  the 
relations  may  become  far  more  complicated  than  with  undamped 
oscillations. 


CHAPTER  V 


RESONANCE  CURVES101 
1.  THE  RESONANCE  CURVE  OF  THE  CURRENT  EFFECT 

70.  General  Remarks. — Assume  two  oscillators  loosely  coupled  and 
let  the  frequency  be  varied  in  one  of  them.  Let  the  current  effect  in 
the  secondary  circuit  be  determined  by  any  suitable  instrument  and  let 
there  be  a  constant  number  of  discharges  per  second.  Plot  the  observed  cur- 
rent effects,  I2e/f,  as  ordinates  and  the  corresponding  frequencies,  Nz,  or 
wave-lengths,  \2,  as  abscissae.  The  curve  thus  obtained  is  called  the 
"resonance  curve  of  the  current  effect."  Theoretically  its  equation  is 


I*.//  =  r- 


1 


(I)* 


FIG.  138. 


i  1.1 

FIG.  139. 


which   is  based  on  the  assumption  that  the  amplitude  curve  of  the 
primary  is  an  exponential  curve  and  that  both  d\  and  di  are  ^2-Tr. 

a.  The  character  of  these  resonance  curves  may  be  seen  from  that 
shown  in  Fig.  138.  At  the  point  JV2  =  Ni  (Ni  =  frequency  of  the  un- 
changed circuit)  the  curve  has  a  very  distinct  maximum — hence  the 
current  effect  is  by  far  greatest  when  both  circuits  have  the  same  fre- 

*S0()  =  Amplitude  of  the  EMF  acting  upon  the  secondary  circuit  =  coLs2x .  /i0 

104 


RESONANCE  CURVES 


105 


quency.     The  abscissa  at  the  peak  of  the  resonance  curve  is  often  called 
the  "point  of  resonance." 

6.  The  value  of  the  ordinate  at  the  peak,  i.e.,  the  size  which  the 
current  effect  in  the  secondary  circuit  reaches,  at  resonance,  depends  upon 
the  decrements  of  the  primary  and  secondary  circuits,  other  things  being 
equal  (similarly  to  the  maximum  amplitude  [Art.  56c]).  The  current 
effect  at  resonance  is  given  by: 

ir\ff  =  r    82fln  l 


and  if  the  primary  oscillations  are  undamped: 


a- 


FIG.  140. 


d22 

In  Fig.  139  curve  a  (as  in  Fig.  122)  corresponds  to  decrements  di  = 
0.08,   d2  =  0.02,   curve  b   (as  in  Fig.    123)  to  dl  =  0.08,  d2  =  0.2.     It 
should  be  noted  that  the  current  ef- 
fect at  resonance  is  much  greater  for 
the  first  than  for  the  second  case. 

c.  The  Sharpness  (Radius  of  Curva- 
ture) of  the  Peak  of  the  Resonance  Curve 
is  of  Importance. — Two  curves  may  be     ^ 
compared  in  this  respect — after  ad- 
j  usting  the  ordinate  scale  of  one  curve     ^ 
— by   superimposing   the  two   maxi- 
mum points,  assuming  that  the  point 
of  resonance  occurs  at  the  same  fre- 
quency  for   both   curves.     If  this  is 
not  the  case,  instead  of  plotting  the 

frequency,  N%,  of  the  varied  circuit,  its  ratio  to  the  frequency  NI  of 
the  unchanged  circuit  is  plotted,  i.e.,  Nz/Ni  and  instead  of  the  cur- 
rent effect  Pef/j  the  values  of  its  ratio  to  the  current  effect  at  resonance, 

J2 

T  lff  ,  are  plotted  as  ordinates. 

ireff 

Then  we  may  state  the  following:  The  peak  of  the  resonance  curve 
will  be  flatter — the  resonance  will  be  less  sharp* — according  as, 

1.  The  sum  of  the  primary  and  secondary  decrements,  di  +  dz,  is 
greater. 

2.  The  coupling  of  the  two  circuits  is  closer. 

In  Fig.  139,  in  which  the  values  of  N%/Ni  are  plotted  as  abscissae, 

*  As  a  measure  of  the  sharpness  of  resonance,  the  reciprocal  value  of  the  dissonance 
[see  Art.  74]  at  which  the  current  effect  is  just  one-half  that  obtained  at  resonance 
may  be  used.  For  the  sharpness  of  resonance,  p,  thus  denned,  Art.  74  gives  the  value 
2ir(di  +  d2)  in  the  case  of  a  normal  resonance  curve;  this  value  is  given  in  Table  XII 
for  different  values  of  di  +  dz. 


106  WIRELESS  TELEGRAPHY 

the  curve  b  (di  +  dz  =  0.28)  has  been  redrawn  as  the  curve  c  by  a  change 
of  scale.  Its  peak  at  resonance  is  much  flatter  than  that  of  the  curve  a, 
which  corresponds  to  the  same  coupling  but  has  a  lower  sum  of  the 
decrements,  di  +  d2  =  0.1.  On  the  other  hand,  the  resonance  curves  a 
and  b  of  Fig.  140  represent  the  same  decrements  with  different  couplings. 
The  curve  b,  which  corresponds  to  the  closer  coupling,  is  somewhat  flatter 
than  a. 

d.  What  has  been  stated  in  regard  to  the  resonance  curves  also  holds, 
at  least  qualitatively,  if  curves  are  plotted  with  the  voltage  effects  or  the 
maximum  amplitudes*  as  ordinates.  Moreover,  in  all  practical  cases, 
these  curves  have  their  maximum  when  the  two  frequencies  are  equal  to 
each  other. 

71.  Measurement  of  the  Frequency. — a.  Principle  of  the  Method 
(O.  LODGE,  H.  HERTZ).  A  condenser  circuit  with  a  known  variable 
frequency,  i.e.,  a  so-called  "measuring  circuit"  is  used.  The  oscillator 
whose  frequency  is  to  be  determined  is  caused  to  act  upon  this  measuring 
circuit,  using  as  loose  a  coupling  as  possible,  and  the  current  indicated  by 
a  measuring  instrument  connected  in  circuit  is  noted  at  different  fre- 
quencies. That  frequency  at  which  the  current  effect  is  a  maximum  is  the 
desired  natural  frequency  of  the  oscillator.102 

Just  how  the  oscillations  are  produced  is  immaterial.  If  the  oscillator 
contains  a  spark  gap,  it  is  simplest  to  use  an  induction  coil,  a  transformer 
or  an  influence  machine.  If  it  contains  no  spark  gap,  and  a  gap  is 
objectionable,  its  oscillations  may  be  induced  by  means  of  either  a 
quenched  gap  circuit  or  by  impulse  excitation  [Art.  78c  and  d,  Art.  109]. 
Under  certain  conditions  it  may  even  be  more  convenient  to  use  the 
measuring  circuit  as  the  primary,  instead  of  as  the  secondary  circuit,  by 
producing  oscillations  in  it,  allowing  it  to  act  inductively  upon  the 
oscillator  through  a  coupling  as  loose  as  possible  and  varying  the  fre- 
quency in  the  measuring  circuit.  The  measuring  instrument  in  this 
case  is  placed  in  the  oscillator,  whose  natural  frequency  is  that  giving 
the  maximum  reading  on  the  instrument. 

b.  For  a  laboratory  measuring  circuit  only  air  or  oil  condensers 
should  be  used.  Air  condensers  of  variable  capacity,  e.g.,  those  de- 
scribed in  Art.  40  are  the  best.f  Very  good  results  are  obtained  by  con- 
necting two  such  condensers  in  parallel,  one  having  large  capacity  for 
the  rough  adjustments  to  resonance,  the  other  having  small  capacity 
for  the  fine  adjustments  and  determination  of  the  points  in  the  resonance 
curve  near  the  peak. 

The  circuit  should  consist  of  closely  wound  coils  having  only  one 

*  These  may  be  measured  by  the  gap  length  they  will  jump  across,  though  to  be 
sure  not  as  accurately  by  far  as  current  or  voltage  effects. 

t  A  condenser  of  fixed  capacity  in  conjunction  with  a  coil  of  variable  self-induction 
(variometer  [Art/38c])  is  less  desirable. 


RESONANCE  CURVES 


107 


layer  of  turns  and  only  one  diameter,  which  must  not  be  small  as  com- 
pared to  the  length  of  the  coil;  the  conductor  is  best  made  of  bands  of 
very  thin  copper  strip  or  braids  of  individually  insulated  very  fine  (e.g., 
0.07  mm.)  copper  wires. 

By  the  use  of  several  interchangeable  coils  the  frequency  may  be 
varied  in  larger  steps,  while  continuous  adjustment  is  obtained  by 
turning  the  plate  condenser's  movable  element. 

c.  The  Measuring  Instrument  in  the  Measuring  Circuit. — Other  things 
being  equal,  the  accuracy  of  a  frequency  determination  increases  with 
the  sharpness  of  the  resonance  curve.  This  sharpness  is  greatest  when 

1.  The  damping  of  the  measuring  circuit  is  lowest  and 

2.  The  coupling  permitted  by  the  measuring  instrument  is  loosest. 
For  both  these  reasons  a  highly  sensitive  instrument  is  best  for  this 


Measuring 
Circuit 


FIG.  141. 

purpose,  in  that  it  requires  very  little  energy  per  second  to  give  a  sufficient 
deflection.  Hence  a  bolometer  and  a  thermal  element  (in  conjunction 
with  a  mirror  galvanometer  or  a  sensitive  needle  galvanometer)  or  a 
thermal  galvanometer  are  preferable  to  the  ordinary  hot-wire  meters 
or  hot-wire-air  thermometers,  if  great  accuracy  is  required  in  the  de- 
terminations. If  the  oscillations  have  very  low  amplitude  [Art.  78d], 
it  is  advisable  to  replace  these  measuring  instruments  by  a  suitable 
detector  [Art.  51]  in  conjunction  with  a  telephone  or  a  sensitive 
galvanometer. 

d.  The  requirement  of  minimum  damping  usually  forbids  the  direct 
connection  of  these  instruments,  which  customarily  have  a  high  resist- 
ance, into  the  measuring  circuit.  Better  results  are  obtained  by  causing 
the  measuring  circuit  to  act  inductively,  through  as  loose  a  coupling  as 
possible,  upon  a  closed  circuit,  the  "indicating  circuit,"  which  contains 
the  measuring  instrument  (Fig.  141). 


108  WIRELESS  TELEGRAPHY 

It  is  advisable  to  make  the  distance  between  the  coupling  coils  Si 
and  £2  (Fig.  141)  variable,  so  that  the  coupling  between  the  measuring 
and  indicating  circuits  may  be  adjusted  at  will.  Furthermore  the  in- 
ductive coupling  between  these  two  circuits  may  be  replaced  by  a  direct 
connection — for  instance  the  measuring  instrument  is  shunted  across 
a  few  turns  in  a  coil  placed  in  the  measuring  circuit. 

If  the  arrangement  is  to  serve  for  all  kinds  of  measurements,*  then 
the  inductance  of  the  indicating  circuit  must  be  made  large  as  com- 
pared to  its  resistance  [Art.  556]. 

e.  In  many  cases,  instead  of  an  indicating  circuit  with  measuring 
instrument,  a  well-known  demonstration  device,  a  GEISSLER  tubej 
parallel  to  the  condenser  in  the  measuring  circuit,  will  serve  the  purpose. 

At  that  frequency  at  which  the  tube  lights,  resonance  exists  between 
the  oscillator,  whose  frequency  is  being  measured,  and  the  measuring 
circuit.  If  the  coupling  is  chosen  sufficiently  loose  so  that  the  tube  just 
begins  to  light  at  resonance  the  determination  can  be  made  about  as 
accurately  as  with  a  commercial  hot-wire  meter  or  hot-wire-air  ther- 
mometer. 

72.  Calibration  of  the  Measuring  Circuit. — Before  determining  un- 
known frequencies  with  a  measuring  circuit  the  latter  must  first  be 
calibrated,  i.e.,  its  own  frequency  determined  for  each  position  of  the 
variable  condenser  and  for  the  different  coils  substituted.105  The 
principle  involved  is  as  follows: 

a.  First  the  condenser  is  calibrated.  Any  method  for  measuring 
capacity  can  be  used  for  this  purpose.  J  The  capacity  is  measured 
for  several  different  positions  of  the  pointer,  and  the  values  found 
arranged  in  tabular  form  or  plotted  as  a  curve,  so  that  the  value  at  any 
position  of  the  pointer  may  be  found  by  interpolation.  For  rotating 
plate  condensers  as  usually  constructed  the  capacity  is  approximately 

C  =  Co  +  a<p  =  a  (<p  +  <po) 

in  which  Co,  a  and  <p0  are  constants,  while  <p  is  the  scale  deflection  of  the 
pointer  at  any  position.  The  calibration  curve  is  therefore  approximately 
a  straight  line. 

b.  The  next  step  is  to  determine  the  frequency  (wave-length)  of  the 
measuring  circuit  for  one  definite  capacity,  i.e.,  one  definite  position  of 
the  pointer  of  the  condenser. 

*  e.g.,  measurements  such  as  are  discussed  in  Art.  87,  et  seq. 

t  The  helium  or  neon  tubes  made  according  to  E.  DoRN103  for  the  observation  of 
electric  oscillations  are  well  adapted  for  this  purpose.  Instead  of  Geissler  tubes,  a 
micrometer  gap,  particularly  as  made  with  two  fine  graphite  electrode  points  is  also 
serviceable. 

{Convenient  methods104  are:  1.  Determination  with  bridge  and  telephone,  if  a 
known  capacity  is  available  for  comparison.  2.  Absolute  determination  with  tuning 
fork  commutator  or  rotating  commutator. 


RESONANCE  CURVES  109 

If  the  frequency,  N  (or  wave-length,  X)  is  known  for  any  one  position 
of  the  condenser,  i.e.,  any  capacity,  C,  then  the  frequency,  N,  for  any 
other  capacity,  Ci,  follows  from 


The  frequencies  (or  wave-lengths)  are  then  calculated  for  a  number  of 
different  condenser  positions  and  a  curve  is  plotted  for  each  test  coil, 
using  the  condenser  scale  readings  as  abscissae  and  the  calculated  fre- 
quencies (or  wave-lengths)  as  ordinates.  The  frequency  or  wave-length 
corresponding  to  any  condenser  position  can  then  be  read  from  these 
curves.* 

c.  The  frequency  of  the  measuring  circuit  for  a  given  capacity  can  at 
times  be  found  by  calculating  the  coefficient  of  self-induction  of  the  test 
coil. 

If  the  test  circuit  consists  of  a  coil  of  one  layer  of  turns,  the  number  of 
turns  being  quite  large  and  if  the  connection  to  the  condenser  is  as  short 
as  possible,  then  the  self-induction  of  the  leads  to  the  condenser  and  of  the 
flow  of  current  in  the  condenser  itself  becomes  negligible  as  compared  to 
the  self-induction  of  the  coil.  The  latter  can  be  calculated  for  direct 
current  from  well-known  formula  (Table  VI)  or  can  be  determined  experi- 
mentally. The  coefficient  of  self-induction  for  rapid  oscillations  is 
very  little  different  from  that  for  direct  current,  if,  by  the  use  of  well 
braided  conductors  of  very  fine  individually  insulated  wires,  the  distri- 
bution of  the  high  frequency  alternating  currents  is  kept  practically  the 
same  as  with  direct  current  [Art.  39]  f.  This  avoids  variation  of  the  coef- 
ficient of  self-induction  with  varying  frequency. 

Otherwise  the  frequency  of  the  measuring  circuit  may  be  determined 
experimentally.  In  order  to  apply  the  methods  which  follow,  a  spark 
gap  (electrodes  of  magnesium,  gap  length  at  least  several  millimeters 
[Art.  5c])  may  be  inserted  and  the  measuring  circuit  fed  by  an  induction 
coil  or  similar  source  of  supply  (Method  1)  or  its  natural  oscillations  may 
be  induced  through  the  use  of  a  quenched  spark-gap  circuit  (Methods  2 
and  3).  Instead  of  this,  it  is  often  more  convenient  to  arrange  an  auxili- 
ary condenser  circuit,  measure  its  frequency  (or  wave-length)  by  one  of 
the  following  methods  and  then  bring  the  measuring  circuit  into  reso- 
nance with  the  auxiliary  condenser  circuit. 

*  It  should  not  be  forgotten  that  the  indicating  circuit  may  influence  the  frequency 
[Art.  55c].  Hence,  either  the  coupling  between  Si  and  S*  (Fig.  141)  must  be  made 
extremely  loose  [Art.  78g]  or,  if  this  does  not  give  a  sufficient  deflection  to  the  instru- 
ment in  the  indicating  circuit,  the  calibration  should  be  carried  out  with  the  same 
coupling  at  which  the  measuring  circuit  will  later  be  used. 

t  The  capacity  of  the  coil  [Art.  736]  must  be  taken  into  consideration  in  case  the 
condenser  has  relatively  small  capacity. 


110  WIRELESS  TELEGRAPHY 

We  have,  then,  the  following  methods  for  determining  the  frequency: 

1.  For  condenser  circuits  with  spark  gap:  photographing  the  spark  in  a 
rotating  mirror  [Art.  2], 

2.  Stationary  Waves  on  Lecher's  Wires. — This  arrangement  (shown  in 
Fig.   142)  is  as  follows:  Two  parallel  wires — whose  distance  apart  is 
very  short  compared  to  their  length — are  bridged  by  a  fixed  cross  strip, 
AB.     A  second  cross  strip,  CD,  is  movable  along  the  wires,  as  is  also  a 
sensitive  Geissler  tube,  G. 

The  condenser  circuit,  I,  whose  frequency  is  to  be  determined,  is 
caused  to  act  inductively  upon  this  system  of  parallel  wires  through  a  very 
loose  coupling.  The  bridge,  CD,  and  the  Geissler  tube,  G,  are  then 
moved,  always  keeping  G  midway  between  AB  and  CD,  until  the  tube 
shows  the  maximum  illumination,  indicating  that  the  circuit  ABCD  is 
in  resonance  with  the  condenser  circuit.  The  curves  of  current  and 


To  Ind.Coil 

FlG.    142. 

potential  distribution  along  the  wires  will  then  be  as  shown  by  I  and  V  in 
Fig.  142*  and  the  distance  AD  =  BC  will  be  a  half  wave-length. f 

If  the  distance  between  the  wires  is  chosen  sufficiently  large  to  make 
the  inductance  considerably  greater  than  the  effective  resistance,  then  the 
velocity,  VL,  of  electromagnetic  waves,  advancing  along  the  double 
wires  is  approximately  106) : 

VL  = 

(L,  C  and  R  are  the  coefficient  of  self-induction,  the  capacity  and  the  re- 
sistance, respectively,  per  unit  length.  From  the  velocity,  VL,  and  the 
wave-length,  X  =  2 AC  =  2BD,  the  frequency  of  the  auxiliary  circuit 
follows  directly  [Art.  19].) 

3.  Combination  of  Calculation  and  Experimental  Methods. — The  main 
portion  of  the  measuring  circuit  is  arranged  in  the  form  of  a  rectangle 

*  The  arrangement  may  be  considered  as  a  combination  of  two  lineal  oscillators 
[Art.  20], 

t  On  the  assumption  that  the  fundamental  oscillation  (and  not  a  partial  wave)  is 
being  observed.  In  case  of  doubt,  it  is  only  necessary  to  move  the  tube,  G,  back  and 
forth  along  the  wires  to  determine  this. 


RESONANCE  CURVES 


111 


i,*  one  of  whose  sides  is  a  movable  cross  strip,  D^EJi  (Fig.  143). 
Upon  this  rectangle,  the  auxiliary  condenser  circuit  (7,  Fig.  143)  is  caused 
to  act  inductively  and  the  condenser,  C,  is  adjusted  so  as  to  bring  the 
measuring  circuit  in  resonance  with  the  auxiliary  condenser  circuit;!  let 
GYi  be  the  capacity  required  for  resonance.  Then  DiEi  is  displaced  to,  say, 
the  position  D2E2,  and  C  is  again  adjusted  for  resonance.  Assume  the 
capacity  needed  for  resonance  in  this  case  to  be  C2.  As  the  frequency 
was  the  same  in  both  cases,  namely,  that  of  the  auxiliary  circuit,  we  have 


iCi    —  L2G  2 

Li  =  C_2 

LZ  GI 


(1) 


in  which  LI  is  the  coefficient  of  self-induction  of  the  measuring  circuit, 
i,  while  L2  is  that  of  the  circuit, 


Th. 


Indicating  Circuit 


O 


\E 


To  Induction  Coil 
FlG.    143. 


Moreover  we  may  write  with  almost  entire  accuracy 

Li  -L2  =  LW-  L^ 


(2) 


in  which  Lf1!  and  LW  represent  the  coefficients  of  self-induction  of  the  rect- 
angles ABDiEi  and  ABD^E^  respectively.    L[1]  and  LW  may  be  calculated 


*  The  self-induction  of  this  rectangle  [Table  VI]  will  be  approximately  the  desired 
circuit  self-inductance. 

t  Resonance  is  observed  by  means  of  the  maximum  indication  of  the  measuring 
instrument  (e.g.,  thermocouple)  in  the  indicating  circuit,  which  latter  must  be  coupled 
extremely  loosely  with  the  measuring  circuit. 


112  WIRELESS  TELEGRAPHY 

from  the  dimensions  (Table  VI).     From  ^  and  LI  —  L2,    the  values  of 

L2 

LI  and  1/2  are  then  obtained,  from  which  the  frequency  follows. 

73.  Determination  of  Capacities  and  Coefficients  of  Self-  and  Mutual 
Induction  by  Resonance.*  —  a.  Self  -inductance,  Capacity  and  Dielectric 
Constants.  —  The  resonance  method  offers  a  very  valuable  and,  particu- 
larly with  the  arrangement  discussed  in  Arts.  7Sd  and  109d,  very 
convenient  means  of  determining  capacities  and  self-inductances.  Va- 
rious methods  of  procedure  are  possible. 

For  instance,  to  measure  the  coefficient  of  self  -inductance,  L,  of  a 
given  circuit  (e.g.,  a  coil),  its  ends  are  connected  to  the  terminals  of  an 
air  condenser  of  known  capacity,  C,  thus  forming  a  condenser  circuit. 
The  natural  frequency,  N,  of  this  circuit  is  then  determined  by  resonance. 

L  then  follows  from  N  = 


If  it  is  only  a  question  of  comparing  the  self-inductance,  LI,  of  a  coil 
with  that,  L2,  of  another  (which,  e.g.,  might  be  a  known  standard  of  self- 
inductance)  then  the  two  coils  are  in  turn  connected  to  a  calibrated  adj  ust- 
able  condenser  through  leads  as  short  as  possible  and  having  no  appre- 
ciable self-inductance  or  capacity;  the  circuit  so  formed  is  then  brought 
into  resonance  with  the  same  auxiliary  circuit  by  adjusting  the  condenser 
in  each  case.  If  C\  and  C2  represent  the  two  capacities,  then  we  have 

N  =  --  ,  ____  =  -    —  ,  ___  t  whence 

2 

LI       C2 


The  capacity  of  a  condenser  would  be  obtained  as  follows.  Its  ter- 
.minals  are  connected  to  a  condenser  circuit,  through  suitable  leads  having 
no  appreciable  capacity  and  a  primary  circuit  is  brought  into  resonance 
with  this.  Then  the  condenser  is  replaced  by  a  variable  calibrated  air 
condenser  which  is  adjusted  until  resonance  is  again  obtained.  This 
value  of  the  variable  air  condenser  is  then  the  desired  capacity  of  the 
unknown  condenser. 

In  this  way,  the  dielectric  constant  of  a  fluid,  e.g.,  an  oil,  may  also  be 
determined.  The  capacity,  C,  of  a  suitable  condenser,  say  of  the  form 
illustrated  in  Fig.  79,  is  measured  with  the  condenser  plates  submerged 
in  the  oil  and  then  with  air  as  the  dielectric,  giving  a  capacity  Co.  Then 
C/Co  is  the  dielectric  constant  of  the  particular  oil.  Only  a  slight  modi- 
fication of  this  procedure  is  necessary  to  adapt  it  to  the  measurement  of 
the  dielectric  constants  of  solid  materials  when  used  in  plate  or  disc 
form. 

The  main  advantage  of  this  resonance  method,  which  may  be  widely 

*  For  a  more  accurate  method  see  Art.  81. 


RESONANCE  CURVES  113 

varied  for  adaptation  to  the  particular  conditions  of  each  individual 
case,  lies  in  the  fact  that  the  self-inductance,  capacity  and  dielectric  con- 
stant can  be  measured  at  the  same  frequency  at  which  they  will  later  be 
used. 

b.  Capacity  of  Coils.  —  Just  as  the  electric  field  between  the  coatings  of 
a  condenser  results  in  a  "  capacity,"  so  the  electric  field  existing  between 
the  various  turns  of  a  coil,  having  different  potentials,  must  give  the  coil 
a  capacity.     This  much  capacity  will  therefore  be  added  to  that  of  the 
condenser  circuit  in  which  the  coil  is  connected. 

Its  determination  may  be  carried  out  as  follows  (A.  MEISSNER23)  : 
The  coil  is  connected  to  an  adjustable  condenser  whose  capacity  must  be 
great  as  compared  to  that  of  the  coil,  and  the  condenser  circuit  so  formed 
is  brought  into  resonance  with  an  auxiliary  circuit.     Then  the  coil  is 
submerged  entirely  in  a  fluid  whose  dielectric  con- 
stant, k,  is  known,  surrounding  the  coil  with  the  fluid 
to  as  great  a  distance  in  all  directions  as  possible.* 
Then  the  variable  capacity  is  reduced  by  an  amount, 
C",   to  again  have  resonance.     It  follows    that  the 

Cr 
effective  capacity  of  the  coil  in  air  is  ,  __  ^  • 

This  measurement  must  under  all  circumstances 
be  made  at  the  same  frequency  at  which  the  coil  will 
later  be  used,  as  the  capacity  of  a  coil  depends  largely 
upon  the  frequency  of  the  alternating  current  passing 
through  it. 

c.  The  coefficient  of  mutual  induction  of  two  coils,  Si  and  S2  (Fig. 
144)  may  also  be  found  by  resonance.     The  two  coils  are  placed  in  the 
relative  position  in  which  their  mutual  induction  is  to  be  determined, 
connected  in  series  (full-line  connection  in  Fig.  144)  and  the  coefficient 
of  self-induction,  Li,  of  the  two  coils  thus  joined  is  measured.     Then  one 
coil  is  reversed  (dotted  lines  in  Fig.  144)  and  the  total  coefficient  of  self- 
induction,  L2,  determined  for  this  condition.     Then  the  coefficient  of 
mutual  induction  is 

T          LI  —  L/2 


74.  Determination  of  the  Sum  of  the  Decrements  of  the  Primary 
and  Secondary  Circuits  (V.  BjERKNES84).  —  a.  In  order  to  determine  the 
decrement  of  an  exponentially  decreasing  oscillation,  the  oscillator  is 
caused  to  act  inductively  upon  a  measuring  circuit  with  variable  fre- 
quency and  through  a  very  loose  coupling  so  as  to  obtain  the  resonance 
curve  [Art.  70].  From  the  latter  the  sum  of  the  decrements  -di  of  the 

*  Say,  by  suspending  the  coil  in  the  middle  of  a  glass  container  or  jar  which  is 
large  compared  to  the  coil. 

8 


114 


WIRELESS  TELEGRAPHY 


oscillator  and  d2  of  the  measuring  circuit  is  obtained  (BJERKNES'S  Reso- 
nance Method). 

How  the  sum  di  +  dz  is  obtained  from  the  resonance  curve,  depends 
upon  what  the  ordinates  and  abscissae  of  the  curve  represent. 

1.  If  the  measuring  circuit  contains  a  variable  condenser,  the  values 
of  its  capacity,  C,  will  usually  be  plotted  as  abscissae,  while  the  ordinates 
would  be  the  current  effect  I2eff  (Fig.  145)  or  the  deflection,  «*  of  a 
measuring  instrument  in  the  indicating  circuit.  Then  we  havef 


=    7T  ' 


(Cr   ~   C) 


\r(Nr) 

FIG.  146. 


in  which  72e//  and  a  represent  current  effect  and  deflection,  respectively, 
when  C  is  the  capacity  in  the  measuring  circuit,  while  /A//,  and  ar  and 
Cr  represent  current  effect,  deflection  and  capacity  at  resonance. 

2.  If  the  measuring  circuit  is  calibrated  in  frequencies,  these  will  be 
used  as  abscissae  with  the  current  effects  or  instrument  deflections  as 
ordinates.  Then  we  have: 

Nr   ~ 


OA 


*  On  condition  that  the  deflection  is  proportional  to  the  current  effect.  For  the 
exact  calibration  see,  e.g.,  B.  S.  LowE.114 

t  The  following  holds  only  for  points  whose  abscissa  is  less  than  that  of  the  point 
of  resonance  (points  to  the  left  of  the  resonance  point  in  Fig.  145).  For  points  to  the 
right  of  the  resonance  point,  a  minus  sign  should  be  placed  before  each  expression. 


RESONANCE  CURVES 


115 


If  the  measuring  circuit  is  calibrated  in  wave-lengths,  X,  and  these  are 
used  as  abscissae  (ordinates  again  °c  ^        then: 


=    27T 


(±^Y- 

\I.tt  I 


3.  In  comparing  different  resonance  curves  it  is  advisable  to  proceed 
as  described  in  Art.  70c.  Having  found  the  frequency,  Nr,  or  wave- 
length, Xr,  and  the  current  effect  I\  eff  at  resonance  between  the  measuring 


circuit  and  oscillator,  the  ratio  jj-  or  ^-  is  plotted  as  abscissa  and  the  ratio 

lY  r          A 


as  ordinate,  the  current  effect  I2eff  corresponding  to  the  frequency 

-I  "r  eff 

N  and  wave-length  X  of  the  measuring  circuit.  Then  the  abscissa  and 
ordinate  of  the  resonance  point  are  taken  as  unity  (x  =  1,  y  =  1)  and  we 
have*  (Fig.  147) : 

*  From  Art.  70  equation  (1)  we  obtain: 

fdi_ 

1 


+ 


if  x 


-. 

Nr 


116  WIRELESS  TELEGRAPHY 


a:  being  the  mean  of  #1  and  xz*  (Fig.  147). 

The  quantity  x  =  -  r  „  ~N~  ~  (or  Xl 

"dissonance"  of  the  two  circuits.     The  value  of  the  factor  A  is  given  in 
Table  XI  for  a  wide  range  of  ordinates.107 

b.  A  simplified  method,  much  used  in  practice  and  usually  of  sufficient 
accuracy,  is  the  following   (H.  BRANDESIOS).     The  instrument  in  the 
measuring  circuit  (or  in  the  very  loosely  coupled  indicating  circuit)  gives 
a  certain  deflection  at  resonance  (capacity  Cr).     The  capacity  is  then 
varied  in  both  directions  until  the  deflection  of  the  instrument  is  just 
half  what  it  was  at  resonance.     Let  C\  and  C%  be  the  capacities  required 
for  this.     Then,  from  par.  (1),  we  have  approximately: 

J        I      J  *        (?!   ""    ^2  n     __        Cl    —  C2 

«i  +  «2  =  2  '     — rj —        =  1-57  •     — ~ — 

If  <t>i,  <pz  and  <pr  represent  the  angles  of  the  scale  readings  of  the  vari- 
able condenser,  corresponding  respectively  to  the  capacities  Ci,  Cz  and 
CT)  we  may  write  the  approximate  relation,  from  Art.  72a  as  follows: 

7,7        1  K7,  <Pi  —  v^t 

di  +  dz  =  1.57 : — 

<pr  -f-  ^>0 

c.  The  relations  given  in  a  and  6  also  hold  if  the  frequency  is  varied 
in  the  primary  circuit  and  the  current  effect  is  measured  in  the  secondary. 
In  that  case  C,  N  and  X  in  the  equations  of  a  and  b  should  be  under- 
stood as  the  variable  quantities  of  the  primary  circuit,  while  Peff  repre- 
sents the  current  effect  in  the  secondary. 

d.  If  the  oscillations  in  the  primary  circuit  are  undamped  the  equations 
of  a  and  b  remain  correct  if  we  put  di  =  0;  the  decrement  of  the  secondary 
circuit  is  then  given  directly. 

75.  Abnormal  Forms  of  the  Resonance  Curves. — In  applying  the 
expressions  given  in  Art.  74  to  different  points  of  an  experimentally 
determined  resonance  curve  it  may  happen  that  the  value  of  d\  +  d^ 
will  be  different  for  different  points,  i.e.,  the  form  of  the  resonance  curve 
is  not  that  assumed  in  Art.  74. 

a.  If  the  value  determined  at  the  various  points  fluctuates  up  and 
down  irregularly,  this  is  due  to  inaccurate  observations  in  obtaining  the 
resonance  curve  (irregular  operation  of  the  interrupter  or  spark  gap). 
All  that  can  be  done  in  such  a  case  is  to  take  the  average  of  the  different 

*  Theoretically  xi  should  =  x2.  In  practice,  however,  because  of  unavoidable 
inaccuracies  in  the  measurements,  x\  and  Xz  will  always  be  slightly  different.  Hence 
it  is' best  to  take  x  the  mean  value  of  xi  and  x2. 

t  A  zero  method  for  determining  the  decrement  has  been  developed  on  this  principle 
by  L.  KANN.109 


RESONANCE  CURVES  117 

values  found  for  di  +  d%;  it  is  preferable,  however,  to  redetermine  the 
resonance  curve. 

b.  If  the  resonance  curve  is  decidedly*  unsymmetrical,  as,  for  instance, 
curve  b  in  Fig.  173,  this  indicates  condenser  leakage  discharge;  the  sum 
of  the  decrements  can  then  not  be  found  at  all  from  the  resonance  curve 
[Art.  86]. 

c.  With  condenser  circuits  having  spark  gaps,  the  following  condition 
is  often  found :  the  resonance  curve  is  symmetrical,  but  the  values  found 
for  di  +  ^2  become  systematically  lower  as  we  go  down  from  the  top  of 
the  curve  (Fig.  148).     An  explanation!  for  this  may  be  that  the  ampli- 
tude curve  of  the  primary  circuit  is  not,  even 

approximately,  an  exponential  curve.110     In  that 
case  the  decrement  does  not  remain  the  same 
during  an  oscillation  [Art.  9c].     If,  in  this  case, 
as  is  usually  done,  the  average  of  the  values 
obtained  at  different  points  is  taken,  t  then  this       f 
mean  value   is   that  value    of   di  +  d2  which     ^ 
would    be    obtained    with   a   condenser   circuit 
having  an  exponential  decrease  of  the  amplitude 
and  giving  the  same  resonance  sharpness. 


This  peculiarity  is  particularly  noticeable  in  FlG   148 

condenser  circuits  having  very  short  spark  gaps. 

With  these,  the  value  obtained  for  d\  and  d%  at  nine-tenths  of  the  height 
of  the  peak  may  be  50  per  cent,  greater  than  that  obtained  at  one- 
third  the  total  height.111  This  is  probably  due,  at  least  in  part,  to 
the  fact  that  the  oscillations  are  abruptly  cut  off  [Art.  9d].  At  any 
rate,  theory  has  shown  (B.  MAddi112)  that  an  abrupt  cutting  off  of  the 
oscillations  may  result  in  a  deformation  of  this  kind  in  the  resonance 
curve. 

d.  It  may  happen  that  the  current  effect  retains  relatively  Targe 
values  for  a  considerable  distance  to  either  side  of  the  resonance  point 
(Fig.  149).  This  may  be  due  to  the  fact  that  the  primary  either  directly 
or  through  some  other  circuit  has  an  inductive  effect  upon  the  indicating 
circuit. 

Or  the  measuring  circuit  may  have  been  coupled  too  closely  with  the 
primary  circuit.  The  resonance  curve  will  then  be  of  the  form  shown 
in  Fig.  150;  the  decrement  values  from  such  a  curve  will  vary  from  point 
to  point  and  be  too  high  throughout.113 

e.  If  the  resonance  curve   has   two  peaks,  this  may  be  taken  as  an 

*  A  slight  dissymmetry  appears  when  the  factor  A  [Art.  556]  is  not  constant, 
depending  upon  the  frequency. 

f  Furthermore  the  instrument  deflections  used  as  ordinates  may  not  be  exactly 
«/».//. 

t  Usually  the  value  obtained  at  one-half  the  total  height  of  the  resonance  curve 
is  identical  with  this  mean  value. 


118 


WIRELESS  TELEGRAPHY 


indication  that  there  are  two  distinct  oscillations  in  the  primary  circuit 
[Fig.  175].  Such  curve  forms,  however  [e.g.,  the  heavy,  full  line  in  Fig. 
151]  may  result  in  quite  another  way,  namely,  if  spark  or  brush  discharges 
pass  between  the  coatings  or  plates  of  the  variable  condensers  (or  at 


FIG.  149. 


FIG.  150. 


other  points  of  the  measuring  circuit).  Thus  in  Fig.  151  the  real  reso- 
nance curve  is  shown  by  the  broken  line:  the  actually  observed  full-line 
curve  having  been  caused  by  a  reduction  of  the  current  effect  at  the  middle 
portion  of  the  curve  due  to  spark  discharges. 

76.  Determination  of  the  Decrements  of  the  Primary  and  Secondary 
Circuits. — a.  With  a  damped  primary  circuit,  the  resonance  curve  gives 
only  the  sum  of  the  decrements  of  the  primary 
and  secondary  circuits.  To  obtain  the  individual 
decrements,  we  may,  for  example,  proceed  as 
follows  (method  of  V.  BjERKNES84).  A  known  re- 
sistance R',  is  connected  into  the  secondary  cir- 
cuit,* which  has  been  brought  into  resonance  with 
the  primary  circuit  (deflection  in  the  indicating  cir- 
cuit =  otr).  This  will  cause  an  increase  in  the 
secondary  decrement  dz  by  an  amount 


A 


FIG.  151. 


(1) 


But  the  instrument  deflection,  dr,  will  be  reduced 


to  a  value  a.     Then 


1 


-t 


-  1 


(2) 


in  which  d  is  the  value  of  di  -f-  d2  obtained  from  the  resonance  curve. 

*  In  the  measuring  circuit  of  Fig.  141,  the  terminals  AB  are  provided  for  this 
purpose. 

t  Assuming  that  the  deflections  <x  72e//.  Otherwise  the  current  effects  must  be 
substituted  for  the  deflections  in  the  equation. 


RESONANCE  CURVES  119 


This  expression  is  simplified  into 

d2  =  d' 


when  df  is  very  small  compared  to  d. 

Having  thus  determined  d2,  the  decrement,  di  of  the  primary  circuit, 
follows  from  the  value  of  di  +  d2  obtained  from  the  resonance  curve. 

b.  It  has  already  been  shown  [Art.  74<i]  that  with  undamped  oscilla- 
tions in  the  primary  circuit  the  decrement  of  the  secondary  can  be  ob- 
tained directly  either  from  the  resonance  curve  or  from  the  simplified 
procedure  of  Art  746.  A  still  simpler  method  may  be  applied  under 
these  conditions.*  First  the  secondary  circuit  is  brought  into  resonance 
with  the  primary.  Assume  that  the  current  effect  in  the  secondary  (or 
in  an  indicating  circuit  coupled  thereto)  =  a.  Then  a  known  resistance, 
R1 ',  is  connected  into  the  secondary  circuit,  thereby  reducing  the  current 
effect  to  a  value  a '.  Then  if  R  represents  the  effective  resistance  of  the 
secondary  circuit  before  R'  was  introduced,  we  have 


Then  the  decrement  follows  from  R  and  Art.  Sd. 

c.  These  methods  of  course  offer  a  means  for  calibrating  the  measuring 
circuit  with  respect  to  the  decrement.  The  values  of  dz  are  found  for  the 
various  current  paths  and  different  condenser  values  and  are  then  listed 
in  tabular  form  or  plotted  as  a  curve. 

In  this  connection  it  should  be  remembered  that  the  decrement  dz 
of  the  measuring  circuit  will  be  affected  by  the  indicating  circuit  unless 
the  coupling  between  them  is  extremely  loose. 

A  sharp  indication  as  to  whether  or  not  this  condition  exists  is  given 
by  the  following.  A  coil  S'i  of  the  same  dimensions  as  Si  is  connected 
between  A  and  B  in  the  measuring  circuit  of  Fig.  141  and  is  caused  to  act 
inductively  upon  another  coil  S'z  having  the  same  dimensions  as  >S2. 
The  distance  between  S'i  and  S'z  is  chosen  the  same  as  that  between  Si 
and  £2.  A  circuit  of  the  same  dimensions  and  resistance  as  the  indicating 
circuit  is  then  constructed  and  joined  to  £'2.  If  this  causes  no  change  in 
the  deflection  of  the  instrument  in  the  indicating  circuit  at  resonance, 

*  For  the  development  of  this  method  as  applied  to  damped  oscillations  (see 
S.  LowE114). 

f  If  the  measuring  instrument  used  gives  the  effective  value  of  the  current,  /,// 

K' 
and  I'eff  respectively,  then  R  =  -j-^ 

le/f  .. 

'  " 


120  WIRELESS  TELEGRAPHY 

then  the  indicating  circuit  has  no  effect  upon  the  decrement  of  the  measur- 
ing circuit. 

This  condition  can  not  be  obtained  when  using  hot-wire  thermometers 
or  commercial  hot-wire  meters,  with  which  the  decrement  is  largely 
dependent  upon  the  indicating  circuit  and  its  degree  of  coupling  to  the 
measuring  circuit.  The  values  of  d2  obtained  in  calibration  therefore 
hold  only  for  those  coils  Si  and  S-2  used  in  calibrating  and  only  for  the  par- 
ticular position  of  those  coils  used  during  calibration. 

77.  Measurement  of  Small  Changes  in  the  Decrement. — The  method 
— change  in  the  current  effect  at  resonance — given  in  Art.  76,  may  also  be 
used  to  advantage  where  small  changes  in  the  decrement  (e.g.,  as  caused 
by  eddy  currents)  are  in  question. 

a.  Equation  (2),  Art.  76,  when  dz  is  known,  i.e.,  with  calibrated  meas- 
uring circuit,  may  be  used  to  determine  any  change  df  in  the  decrement, 
whether  in  the  primary  or  in  the  secondary  circuit.     This  gives  the 
decrement  change  with  much  greater  accuracy  than  by  obtaining  it 
from  the  resonance  curve.* 

b.  Sometimes,  particularly  for  comparisons,  it  is  very  convenient  to 
use  the  "equivalent  resistance,"  instead  of  the  change  in  the  decrement, 
d' ',  produced  by  some  such  cause  as  e.g.,  eddy  currents.     The  equivalent 
resistance  is  that  resistance,  R',  which  would  have  to  be  connected  into 
the  circuit  to  increase  the  decrement  by  d'. 

This  equivalent  resistance,.  R',  can  be  calculated  from  equation  (1), 
Art.  76,  i.e.,  from  the  measured  increase  of  the  decrement,  d',  and  the 
dimensions  of  the  circuit.114 

If  only  Rf  is  desired,  it  is  much  simpler  to  apply  the  method  given 
above  as  a  compensation  method.  For  instance,  assume  a  conductor 
brought  near  the  secondary  circuit  has  caused  a  reduction  of  the  deflec- 
tion in  the  indicating  circuit  from  a  to  a.  To  determine  its  equivalent 
resistance,  the  conductor  is  removed  and  resistance  inserted  in  the 
secondary  circuit  until  the  deflection  at  resonance  again  falls  from  ar  to 
a'.f  The  resistance  having  this  effect  is  R'. 

78.  Measurements  with  Resonance  Circuits  in  General. — a.  For  the 
excitation  or  production  of  the  oscillations  in  the  primary  circuit,  four 
methods  are  available  in  the  laboratory,  viz. : 

1.  Undamped  oscillations  by  the  arc  method. 

2.  Excitation  by  a  quenched  spark-gap  circuit  (Fig.  152). 

3.  Impulse  excitation  [d]. 

*  Other  things  being  equal,  the  accuracy  of  the  determination  increases  as  the 
sum  of  the  decrements  of  the  primary  and  secondary  decreases;  hence  it  is  advisable 
to  use  a  quenched  spark-gap  circuit  for  producing  the  oscillations  [Art.  78c]. 

f  The  frequency  may  be  influenced  by  the  eddy  currents  in  which  case  it  must  be 
brought  back  to  its  original  value  by  suitable  regulation. 


RESONANCE  CURVES 


121 


4.  Charging  the  condenser  in  the  primary  circuit  and  discharging 
through  a  spark  gap. 

The  requisite  condition  underlying  the  equations  of  Arts.  70,  74  and 
76  are: 

1.  The  primary  oscillation  must  be  of  constant  frequency. 

2.  The  amplitude  curve  must  be  either  a  straight  line  parallel  to  the 
axis  of  abscissae  (undamped  oscillations)  or  an  exponential  curve. 

None  of  the  methods  of  excitation  given  above  strictly  fulfills  both  re- 
quirements. The  form  of  the  resonance  curve  gives  some  indication  of 
how  nearly  they  are  fulfilled  [Art.  75].  Hence  even  when  the  measure- 
ments do  not  absolutely  necessitate  it,  it  is  advisable  to  plot  the 
resonance  curve. 

To  these  requirements  should  be  added  another,  of  great  practical 
importance,  viz.,  constant  amplitude  and  frequency  of  discharge.  If 
these  are  not  constant,  the  fluctuations  of  the  instruments  will  prevent 
accurate  measurements  [also  see  g]. 


Quenched  Gap  Circuit 


Measuri 


FIG.  152. 

b.  The  presence  of  upper  harmonic  oscillations  of  higher  frequency  in 
addition  to  the  fundamental,  when  using  the  arc  method  for  undamped 
oscillations  (Chap.  IX115)  does  not  generally  interfere  if  the  secondary  is 
a  condenser  circuit.*  But  if  the  frequency  of  the  fundamental  oscilla- 
tion is  not  entirely  constant,  its  fluctuations  will  cause  a  widening  of  the 
resonance  curve  and  application  of  the  equations  of  Art.  74  will  give  too 
high  a  value  for  the  decrement.  The  errors,  however,  which  occur  in 
this  way  with  arcs  especially  intended  for  measurements  [Art.  125],  once 
skill  is  attained  in  their  manipulation,  are  not  large.  But,  what  is  most 
unsatisfactory,  is  not  so  much  the  average  amount  of  the  error  as  the  un- 
certainty of  its  extent  at  any  particular  instant.  Another  disadvantage 
of  the  arc  method  is  the  difficulty  of  keeping  the  amplitude  sufficiently 
constant. 

Otherwise,  measurements,  particularly  of  the  decrement,  are  espe- 
cially convenient  and  simple  with  undamped  oscillations. 

*  With  an  open  secondary  circuit  (antenna)  this  may  cause  disturbance  if  an 
upper  harmonic  of  the  secondary  should  happen  to  be  in  resonance  with  an  upper 
harmonic  of  the  primary  circuit. 


122  WIRELESS  TELEGRAPHY 

c.  If  the  primary  oscillations  are  induced  by  means  of  a  quenched 
spark-gap  circuit,  then  from  the  moment  the  oscillations  in  the  gap  cir- 
cuit stop,  those  in  the  primary  circuit  fulfill  the  requirements  given  above, 
viz.,  the  frequency  is  absolutely  constant,  the  amplitude  curve  is  an  expo- 
nential curve.*     Hence  the  resonance  curves  obtained  by  this  method 
have  the  normal  form  as  shown  in  Art.  74. 

Excitation  by  means  of  a  quenched  gap  circuit^  moreover,  has  the 
great  advantage  that  the  oscillations  in  the  primary  circuit  are  much  less 
damped  than  they  would  be  if  the  primary  circuit  included  a  spark  gap. 
In  addition,  a  very  high  number  of  discharges  per  second  may  be  used. 
This  increases  the  current  effect  to  such  ah  extent  that  the  coupling 
between  the  primary  and  the  measuring  circuit  and  also  between  the  latter 
and  the  indicating  circuit,  if  one  is  used,  may  be  made  very  loose. 

The  regularity  of  the  oscillations  depends  upon  the  kind  of  gap  used. 
The  mercury  arc  lamp  and  especially  series  gaps  in  hydrogen  are  well 
adapted  for  the  purpose.  Also  the  series  spark  gap  of  TELEFUNKEN 
with  disc-shaped  silver  electrodes  in  air  [Art.  lllc],  as  well  as  PEUCKERT'S 
generator  [Art.  llle]  can  be  used  to  advantage.116  They  are  suitably 
operated  by  an  alternating-current  transformer  (also  an  induction  coil  fed 
by  alternating  current) ,  or  a  resonance  coil. 

d.  The  third  method  impulse  excitation  of  the  primary  circuit  [Art. 
109d]  is  experimentally  of  extreme  simplicity:  a  storage  battery  of  a  few 
cells  and  a  suitable  interrupter  giving  a  high  number  of  interruptions  per 
second  are  all  that  is  needed  to  produce  the  oscillations.     To  determine 
resonance  in  the  secondary  circuit  a  detector  [Art.  51]  with  telephone  or 
galvanometer  is  used,  the  simplest  kind  of  detector,  such  as,  e.g.,  is  quickly 
made  from  a  piece  of  galena  and  a  point  of  graphite  pressed  lightly 
against  the  galena  by  a  spring,  suffices  entirely.     If  the  primary  circuit  is 
properly  designed,  its  oscillations  will  be  only  very  slightly  damped.     The 
high  sensitiveness  of  the  detector  and  the  fact  that  the  current  effect 
(even  though  the  oscillations  have  a  small  amplitude)  is  relatively  large 
on  account  of  the  high  number  of  discharges  per  second,  permit  extremely 
loose  coupling  between  the  primary  and  secondary  circuits.     Hence  the 
various  measurements  based  on  the  resonance  principle  [Art.  73]  can  be 
made  with  this  method  just  as  accurately  as  with  any  method  using  the 
current  effect. 

For  determinations  of  the  decrement  from  the  resonance  curve,  this 
method  is  suitable  only  if  the  detector  works  with  great  regularity  and  is 
calibrated. 

e.  The  fourth  method,  namely,  charging  the  condenser  in  the  primary 
circuit  and  allowing  it  to  discharge  through  a  spark  gap  [Art.  1],  has  the 

*  The  presence  of  two  oscillations  up  to  this  moment  will  interfere  less  as  the 
coupling  to  the  quenched  gap  circuit  is  made  closer,  i.e.,  the  faster  the  oscillations  in 
the  latter  die  out.191 


RESONANCE  CURVES  123 

advantage  that  the  amplitude  can  be  very  easily  varied  over  wide  limits ; 
its  disadvantage  lies  in  the  fact  that  the  amplitude  curve  of  the  resultant 
oscillations  does  not  approximate  an  exponential  curve.  Moreover  the 
discontinuing  of  the  oscillations  in  the  primary  circuit  at  a  certain  instant 
and  the  fact  that  the  spark  gap  affects  even  the  frequency  [Art.  9]  must 
be  taken  into  consideration.  Entirely  aside  from  the  questionable  value 
of  determinations  of  the  decrement  of  the  primary  circuit  by  this  method, 
it  is  very  doubtful  to  what  extent  we  may  draw  conclusions  from  the 
resonance  curve  under  these  circumstances  as  to  the  decrement  of  the 
secondary  circuit. 

On  the  other  hand,  a  great  many  determinations  have  shown  that  this 
method  is  entirely  accurate  for  frequency  measurements  and  gives  at 
least  approximately  correct  results  for  secondary  decrements,  on  condition 
that  such  spark  gaps  as  have  been  found  to  cause  wide  variations  from 
the  conditions  existing  in  condenser  circuits  having  no  spark  gap  are 
avoided,  i.e.,  spark  gaps  less  than  5  mm.  long  and  having  copper  or  silver 
electrodes.  Furthermore  the  following  should  be  considered  in  regard  to 
the  primary  circuit.  The  average  value  of  d\,  obtained  from  the  resonance 
curve  [Art.  75c],  does  not  correctly  characterize  the  decrease  with  time  of 
the  amplitude  in  the  primary,  but  defines  with  sufficient  accuracy  the 
shape  of  the  resonance  curve  and  hence  the  sharpness  of  resonance  and 
the  maximum  current  effect  attainable  with  the  particular  primary  circuit 
in  a  loosely  coupled  secondary.  But  these  are  just  the  quantities  on 
account  of  which  the  decrement  is  of  practical  interest.  The  decrease  in 
the  amplitude  itself  is  only  of  minor  importance  in  practice. 

To  obtain  the  greatest  possible  regularity  in  the  discharges  only  a  low 
number  of  sparks  per  second  should  be  used  and  partial  spark  discharges 
be  avoided,  assuming  the  use  of  metallic  spark  gaps  in  air.  *  Magnesium 
is  the  best  electrode  material  in  air;  tin,  zinc  and  aluminium  are  less 
suitable;  copper  and  silver  are  especially  bad  for  the  purpose. 

The  regularity  of  the  sparks  is  affected  by  retardation  of  the  discharge 
[Art/426],  so  that  all  means  for  reducing  the  retardation  tend  to  increase 
the  regularity.  Subjecting  the  gap  to  ultra-violet  light  has  already  been 
mentioned  in  Art.  426  as  one  such  means.  Another  method  is  to  attach 
a  fine  point  (say  a  pointed  wire)  to  one  electrode  (Fig.  153).  The  position 
of  the  point  can  be  so  adjusted  until  the  point  discharge  causes  a  very 
regular  main  discharge  without  materially  changing  the  potential  ampli- 
tude (W.  EicKHOFF118).  If  magnesium  electrodes  are  used,  however,  this 
method  usually  need  not  be  applied.  An  induction  coil  with  D.C.  supply 

*  If  a  mercury  arc  lamp117  or  a  metallic  gap  in  hydrogen  is  used,  many  partial 
spark  discharges  may  be  used  without  resulting  in  irregularities;  in  this  way  the  current 
effect  can  be  greatly  increased.  However,  the  much  higher  damping  of  such  spark 
gaps  is  the  bad  part  of  the  bargain. 


124 


WIRELESS  TELEGRAPHY 


and  a  mercury-turbine  interrupter*  or  a  large  influence  machine,  but, 
best  of  all  by  far,  a  resonance  coil  with  A.C.  supply  [Art.  114a]  serve  as 
suitable  current  sources. 

/.  For  the  measuring  circuit  minimum  damping  offers  the  advantage 
that  the  frequency,  due  to  the  increased  sharpness  of  resonance,  as  well 
as  the  decrement  of  any  primary  circuit  can  both  be  more  accurately 
determined,  other  things  being  equal. 

If  it  is  to  be  expected  that  the  primary  oscillations  will  be  of  relatively 
short  duration  (short  spark  gaps)  then  it  would  seem  advisable  to  make 
the  decrement  of  the  measuring  circuit  about  equal  to  that  of  the  pri- 
mary circuit.112 

g.  To  the  requirements  of  a  should  be  added  the  very  important  one : 
the  coupling  between  primary  and  secondary  circuits  must  be  extremely 
loose,  i.e.,  so  loose  that  there  is  no  appreciable  reaction. 


To  Source  of  Current 


FIG.  153. 


FIG.  154. 


Whether  or  not  that  is  the  case,  can  be  determined  as  follows.  Con- 
struct a  condenser  circuit  (///,  Fig.  154)  of  about  the  same  dimensions 
as  the  secondary  circuit  and  coupled  to  the  primary  circuit  about  as 
closely  as  the  secondary  is.  If  this  causes  no  change  in  the  current  effect 
in  the  secondary  at  resonance,  it  follows  that  no  appreciable  reaction 
exists  between  the  secondary  and  primary  circuits.119 

Commercial  wave  meters  have  sacrificed  the  fulfillment  of  these 
various  requirements  in  order  to  make  use  of  the  convenient  but  rela- 
tively non-sensitive  commercial  measuring  instruments.  Hence  the 
values  for  di  +  d%  [Art.  74]  and  for  d%  [Art.  76]  obtained  by  them  are,  in 
general,  too  large.  The  error  may  amount  to  even  30  per  cent.120  It  can 
be  decreased  by  increasing  the  current  effect  in  the  primary,  as  this  allows 
a  looser  coupling  to  obtain  a  sufficient  deflection  in  the  indicating  circuit. 

h.  The  wires  leading  to  the  current  source  (e.g.,  transformer)  must  be 
connected  directly  at  the  terminals  of  the  spark  gap  (thus  in  Fig.  2,  at 

*  It  is  advisable  to  use  a  motor  of  somewhat  larger  capacity  than  that  generally 
supplied  by  the  manufacturers  and  to  mount  a  fly-wheel  on  its  axis. 


RESONANCE  CURVES  125 

the  points  FI  and  F2,  and  not  at  A  and  B) ,  as  otherwise  the  damping  of 
the  primary  circuit  may  be  considerably  increased. 

i.  If  a  revolving  coil,  mirror  galvanometer  is  used  in  the  indicating 
circuit,  it  is  usually  advisable  to  ground  the  coil.  Otherwise  the  coil 
may  become  charged  and  react  similarly  to  the  needle  of  a  quadrant 
electrometer. 

79.  Commercial  "Wave  Meters".121 — a.  Wave  meters,  which  are 
simply  commercial  constructions  of  the  measuring  circuits  described  in 
Art.  71,  are  arranged  for  one  or  more  of  the  following  duties: 

1.  Determination  of  the   natural  frequency   of   any   oscillator   and 
through  this,  of  the  capacity,  the  self-inductance,  the  mutual  inductance 
[Art.  73],  and  the  degree  of  coupling  [Art.  87]. 

2.  Determination  of  the  decrement  of  any  circuit. 

3.  Production  of  oscillations  of  any  desired  frequency  (the  wave  meter 
used  as  primary  circuit). 

These  are  all  based  on  the  resonance  principle  described  in  Arts. 
70  and  74.  Hence  the  essential  part  is  a  condenser  circuit  whose  fre- 
quency can  be  continuously  varied  over  a  known  range.  For  this  purpose 
wave  meters  have  either 

1.  A  condenser  of  continuously  variable  capacity  and  one  or   more 
coils    of    fixed    self-inductance    (e.g.,    TELEFUNKEN    Co.,122    MARCONI 
Co.123),  or 

2.  One  or  more  condensers  of  fixed  capacity  and  a  coil  of  variable 
self-inductance   (" variometer")    (e.g.,   G.   SEIBT   [C.   LoRENZ124],    IVES, 
DE  FOREST),  or  finally 

3.  Both  capacity  and  self-inductance  are  variable,  in  some  cases  the 
movable  parts  of  the  condenser  and  the  inductive  coil  being  linked  so 
as  to  move  in  unison  (e.g.,  J.  A.  FLEMING'S  Kymometer,125  PERi126). 

The  movable  parts  are  usually  provided  with  a  pointer  moving  over 
a  scale,  which  mostly  permits  a  direct  reading  of  the  wave-length  (or 
frequency)  at  each  position  of  the  pointer. 

6.  To  measure  the  frequency  (or  wave-length)  of  an  oscillator,  e.g.,  a 
condenser  circuit,  the  wave  meter  is  set  up  near  it  and  the  wave  meter's 
frequency  varied  until  it  is  in  resonance  with  the  oscillator.  Resonance 
is  indicated  either  by 

1.  The  lighting  of  a  Geissler  tube,  or 

2.  The  maximum  deflection  of  a  measuring  instrument  (e.g.,  hot- 
wire meter)  connected  directly  into  the  measuring  circuit  or  coupled  to  it, 
or 

3.  The  maximum  sound  intensity  in  a  telephone  which  is  connected, 
together  with  a  detector,  in  parallel  to  a  portion  of  the  measuring  circuit 
or  which  is  in  a  separate  indicating  circuit. 

Some  wave  meters  have  several  of  these  arrangements  provided  at  the 
same  time. 


126 


WIRELESS  TELEGRAPHY 


c.  The  decrement  of  an  oscillator  is  rarely  determined  in  practice  by 
the  resonance  curve  method  of  Art.  74a,  it  being  customary  to  employ 
the  simplified  method  given  in  Art.  746,  using  the  measuring  instrument 
mentioned  in  62  [Art.  79].  Both  methods  give  the  sum  of  the  decrements 
of  the  oscillator  and  the  measuring  circuit;  the  latter  either  being  known 
or  found  as  per  Art.  76,  the  oscillator  decrement  follows. 

Another  method,123  which  gives  approximate  values  of  the  decrement 
without  the  use  of  an  actual  measuring  instrument,  only  employing  a 
detector  and  telephone,  is  that  used  in  the  MARCONI  "Decremeter." 
It  is  based  on  the  equation  of  Art.  74a2, 


Nr-  N 
Nr 


I 


Vfef 


The  arrangement  is  shown  diagrammatically  in  Fig.  155.  The 
measuring  circuit  contains  a  variable  condenser,  C,  a  self-inductance,  L, 
a  small  coil,  L3,  which  can  be  either  connected  into  the  circuit  or  else  short- 
circuited,  and  a  coil,  L2,  having  thirty-two  turns  of  heavy  wire.  The 
coefficient  of  self-inductance  of  L3  is  so  chosen  that  by  the  introduction 

of  this  coil  the  frequency  of  the 
measuring  circuit  is  changed 
by  4  per  cent.,  this  change,  as 
shown  in  Art.  3,  being  indepen- 
dent of  the  capacity  of  the  cir- 
cuit. The  detector,  D,  and 
the  telephone,  T,  with  the  cell, 
E,  are  shunted  across  the  coil 
/2  from  its  end  A  to  the  sliding 
contact  S. 

In  order  to  determine  the 
decrement  of  an  oscillator  the 
measuring  circuit,  without  the 
coil  La,  is  first  brought  into 
resonance  with  the  oscillator  (maximum  sound  intensity  in  the  tele- 
phone). Then: 

1.  The  measuring  circuit  is  put  out  of  resonance  to  the  extent  of  4 
per  cent,  by  inserting  L3,  and  the  tone  in  the  telephone  noted  with  the 
sliding  contact  at  B,  i.e.,  with  thirty-two  turns  of  L2  in  circuit.     Let  /2e// 
be  the  current  effect  in  the  measuring  circuit  under  these  conditions. 

2.  The  coil  L3  is  again  cut  out,  bringing  the  measuring  circuit  into 
resonance  again.     The  sliding  contact  is  then  displaced  until  the  tone  in 
the  telephone  is  just  as  loud  as  it  was  in  1.     Let  n  be  the  number  of  turns 
now  between  A  and  St  and  let  7r2e//  be  the  current  effect  in  the  measuring 


FIG.  155. 


RESONANCE  CURVES 


127 


circuit.     Provision  is  made  by  suitable  arrangements  for  quickly  obtain- 
ing the  conditions  of  1  and  2. 

In  the  arrangement  of  Fig.  155,  the  current  amplitude  in  the  detec- 
tor during  each  period  is  proportional  to  the  current  amplitude  in  the 
measuring  circuit  and  to  the  number  of  turns  in  parallel  with  the  detec- 
tor. Hence  the  current  effect  in  the  detector  must  be  proportional  to 
the  current  effect  in  the  measuring  circuit  and  to  the  square  of  the  number 
of  parallel  turns.  Therefore,  if  the  detector  action  depends  upon  the 
current  effect,  and  if  the  tone  in  the  telephone  and  therefore  the  current 
effect  in  the  detector  is  the  same  in  both  cases  1  and  2,  then  we  have 


FIG.  156. 


/  J^lL\   _  /  —  \  .     Applying  this  to  Art.  74a2,  we  obtain  the  sum  of  the 
\  1  eff  I        \n  / 

decrements  of  the  oscillator  and  the  measuring  circuit  : 


X 


0.04J 


(f  >  - ' 


d.  In  order  to  use  a  wave  meter  as  a  primary  circuit,  either 

1.  Small  spark  gaps  are  inserted  in  it  so  that  oscillations  may  be  pro- 
duced by  means  of  an  induction  coil,  or 

2.  Means  are  provided  for  producing  oscillations  by  impulse  excita- 
tion [Art.  109]. 

e.  Only  a  few  of  the  many  types  of  commercial  wave  meters  can  be 
described  here.     Probably  that  of  J.  ZENNECK127  was  the  first  used  in 


128 


WIRELESS  TELEGRAPHY 


FIG.  157. 


FIG.  158. 


RESONANCE  CURVES 


129 


wireless  telegraphy.  It  consisted  of  a  condenser  of  fixed  capacity  and 
continuously  variable  self-inductance.  A  Geissler  tube  or  a  spark  gap 
served  for  frequency  measurements  by  means  of  resonance,  while  a 
bolometer  was  used  for  decrement  determinations. 

The  next  step  in  this  direction  is  represented  by  the  FRANKE-DONITZ 
(Telefunken)  wave  meter  shown  in  Fig.  156;  it  consisted  of  a  variable 
condenser,  interchangeable  coils  for  the  different  ranges  and  a  hot-wire- 
air  thermometer.  Very  similar  in  design  and  equally  simple  is  the  port- 


FIG.  159. 


able  wave  meter  of  the  MARCONI  Co.,  of  which  Fig.  157  shows  the  con- 
nections diagrammatically,  Fig.  158  the  finished  construction;  it  consists 
of  a  variable  condenser,  a  fixed  self-inductance  of  rectangular  shape 
mounted  into  the  cover  of  the  case  and  a  carborundum  detector  [Ait. 
160]  with  telephone. 

The  later  wave  meter  of  the  TELEFUNKEN  Co.  (Fig.  159)  whose  adjust- 
able condenser,  in  addition  to  its  graduated  scale,  also  has  three  scales 
of  wave-lengths  corresponding  to  the  different  coils,  while  more  compli- 
cated, has  a  much  wider  range  of  usefulness.  The  same  applies  to  the 
portable  decremeter  of  the  MARCONI  Co.  (Fig.  160). 


130 


WIRELESS  TELEGRAPHY 


f.  The  direct-reading  wave  meter  of  R.  HiRSCH*'128  is  based  upon  a 
very  neat  application  of  the  resonance  principle. 


FIG.  160. 


a 


C1 


1  / 


FIG.  161. 


FIG.  162. 


*  Manufactured  by  DR.  E.  HUTH,  G.  M.  B.  H.,  Berlin,  to  whom  the  author  is 
indebted  for  the  cuts. 


RESONANCE  CURVES 


131 


FIG.  163. 


FIG.  164. 


132 


WIRELESS  TELEGRAPHY 


The  measuring  circuit  (Figs.  161  and  162)  consists  of  a  fixed  self-induc- 
tance, L,  and  a  variable  condenser  having  one  fixed,  C,  and  one  movable, 
C1,  set  of  plates,  the  latter  being  rotated  by  a  motor.  This  also  rotates  a 
small  helium  tube,  A,  over  a  scale,  B,  the  tube  being  connected  in  parallel 
with  the  condenser.  The  rotation  of  the  movable  element  of  the  con- 
denser causes  a  continuous  variation  in  the  frequency  of  the  measuring 
circuit.  At  that  position  at  which  the  measuring  circuit  is  in  resonance 
with  the  oscillator  under  observation,  the  tube  becomes  illuminated  and 
a  bright  line  is  seen  on  the  scale  at  the  point  where  the  helium  tube  is  at 
the  instant  of  resonance.  By  indicating  along  the  scale  the  wave-lengths 
of  the  measuring  circuit  corresponding  to  each  position  of  the  rotating 
element,  the  instrument  becomes  direct-reading0  Two  forms  of  this 
wave  meter  are  shown  in  Figs.  163  and  164. 


2.  RESONANCE  CURVE  OF  THE  DYNAMOMETER  EFFECT 

(L.  MANDELSTAM  AND  N.  PAPALEXi129) 

80.  General. — a.  Assume  a  movable  coil,  $2,  in  a  vertical  plane,  e.g., 
suspended  on  a  vertical  wire,  placed  within  a  fixed  coil,  Si,  also  in  a  ver- 
tical plane.  If  a  current  /i  is  passed  through  Si  and  /2  through  $2,  the 

turning    moment    to    which    the 
/|\  movable  coil  is  subjected    ^Iil^. 

If  /i  and  72  vary  rapidly  with 
time,  as  e.g.,  in  high  frequency 
alternating  currents,  the  coil  will 
in  general  not  respond  to  the 
rapid  variations  and  its  motion 
will  be  determined  by  the  average 

FIG.  165.  turning  moment,  i.e.,  the  average 

value  of  /i/g.     This  average  value 

is  called  the  "dynamometer  effect,"  IiI2130,  from  the  use  of  this  arrange- 
ment of  a  movable  coil  in  the  field  of  a  fixed  coil  in  the  well-known 
dynamometer  type  of  wattmeters.  This  arrangement  also  always  makes 
it  possible  to  measure  IiI2. 

b.  Assume  now,  as  in  Art.  70,  that  a  primary  circuit  of  constant  fre- 
quency (and  wave-length)  acts  inductively  upon  a  secondary  circuit 
of  variable  wave-length,  e.g.,  an  adjustable  condenser  circuit.  Let  I\ 
and  72  represent  the  currents  in  the  primary  and  secondary  circuits  re- 
spectively. The  dynamometer  effect  of  the  two  currents  is  measured 
and  a  curve  plotted  in  which  the  abscissae  are  the  wave-lengths  (or 
capacities)  of  the  variable  secondary  circuit,  the  ordinates  being  the 
corresponding  dynamometer  effects. 

The  resulting  curve  will  be  of  the  form  shown  in  Fig.  165;  as  may  be 
shown  theoretically129  this  curve  passes  through  the  axis  of  abscissae  when 


RESONANCE  CURVES 


133 


the  wave-length  of  the  secondary  circuit  is  equal  to  that  of  the  primary, 
i.e.,  when  the  two  circuits  are  in  resonance. 

c.  The  form  of  this  resonance  curve,  similarly  to  the  current  effect 
curve  [Art.  70c]  depends  on: 

1.  The  sum  of  the  decrements  of  the  primary  and  secondary  circuits. 

2.  The  degree  of  coupling  between  the  two  circuits. 


FIG.  166. 


FIG.  167. 


The  effect  of  the  size  of  the  decrement  is  shown  by  curves  /  and  //  of 
Fig.  166*  and  the  effect  of  the  percentage  of  coupling  is  shown  by  curves  I 
and  II  of  Fig.  167. |  In  these  curves  the  abscissae  are  the  dissonance 
values, 

\        \  r        r 

A.2     —    I\T  -t    /    ^2    ~"~~    ^  T 

/2~cT 


x  = 


X, 


I 


X' 


X" 


FIG.  168. 


d.  If  the  coupling  between  primary  and  secondary  circuits  is  extremely 
loose,  we  have  the  following  relations  (Fig.  168)  : 

1.  Let  xi  and  x2  be  the  dissonance  values  at  which  the  dynamometer 
effect  has  its  maximum  positive  and  negative  values  respectively.  Then 


=    27T 


*  /  :di  =  0.05,  d2  =  0.01;  II  :di  =  d2  =  0.01. 

t  di  =  0.05,  dz  =  0.01;  7  :  coupling  extremely  loose;  II  :K'  =  0.3  per  cent. 


134  WIRELESS  TELEGRAPHY 

2.  If  a  line  is  drawn  parallel  to  the  axis  of  abscissae  and  intersecting  the 
resonance  curve  at  the  points  whose  abscissae  are  x'  and  x",  then 


81.  Determination  of  the  Frequency  (Wave-length).  —  a.  A  method 
for  determining  the  frequency  (wave-length)  of  a  primary  circuit  follows 
directly  from  Art.  806.  The  primary  is  caused  to  act  inductively  upon  a 
measuring  circuit  through  an  extremely  loose  coupling  and  the  dynamome- 
ter effect  7  1/2  of  the  primary  current  l\  and  the  measuring  current  72  is 
measured.  The  frequency  of  the  measuring  circuit  is  varied  until  the 
dynamometer  effect  becomes  zero.  That  frequency  (wave-length)  of  the 
measuring  circuit  at  which  this  occurs  is  the  desired  frequency  of  the 
primary  circuit. 

b.  Instead  of  leading  the  primary  and  measuring  currents  directly 
through  the  dynamometer,  it  is  more  convenient  to  have  both  circuits  act 


Dynamometer 
FIG.  169. 

inductively,  through  as  loose  a  coupling  as  possible,  upon  two  coils,  Si  and 
$2  (Fig.  169)  which  are  connected  to  the  dynamometer.  It  can  be 
shown129  that  the  dynamometer  effect  /'i/'2  of  the  currents  induced  in 
these  coils  follows  practically  the  same  changes  as  /i/2- 

c.  Wave-length  (or  frequency)  determination  by  means  of  the  dyna- 
mometer effect  has  the  following  advantages  over  the  determination  by 
means  of  the  current  effect  [Art.  71]. 

1.  It  is  much  more  accurate.  In  the  current  effect  method  we  work 
around  the  peak  of  the  resonance  curve  and  slight  variations  in  the 
frequency  cause  but  very  slight  (percentage)  changes  in  the  deflection. 
Hence,  in  order  to  obtain  the  exact  point  of  resonance  it  becomes  prac- 
tically essential  to  plot  the  resonance  curve  or  at  least  its  upper  part.  The 
dynamometer  determination,  on  the  other  hand,  is  a  zero  method.  The 
slightest  deviation  from  resonance  produces  a  noticeable  deflection  in 


RESONANCE  CURVES  135 

the  measuring  instrument.  The  dynamometer  method  is  therefore  to 
be  used  wherever  small  changes  in  the  frequency  (or  in  the  capacity,  dielec- 
tric constant  or  coefficient  of  self-induction  [Art.  73])  are  to  be  measured  ; 
in  accuracy  it  surpasses  by  far  all  other  methods. 

2.  The  accuracy  of  frequency  determinations  by  means  of  the  current 
effect  method,  depends  upon  the  accuracy  with  which  the  resonance  curve 
can  be  obtained,  i.e.,  upon  the  regularity  of  the  discharges  per  second  and 
the  amplitude.  The  dynamometer  method  is  independent  of  both  these 
factors. 

82.  Decrement  Determination.  —  This  is  based  upon  the  relations 
described  in  Art.  8Qd.  As  in  the  case  of  the  current  effect  method,  the  sum 
of  the  primary  and  secondary  decrements  is  obtained.  The  connections 
are  those  shown  in  Fig.  169,  with  the  stipulation  that  the  coupling  between 
the  primary  and  measuring  circuits  must  be  extremely  loose. 

a.  To  find  the  sum  of  the  decrements  by  Art.  SOdl,  the  wave-length,  X 
(capacity,  C)  of  the  measuring  circuit  is  varied  until  the  dynamometer 
effect  is  a  maximum  either  on  the  positive  (X  =  Xi,  C  =  Ci)  or  the  nega- 
tive (X  =  X2,  C  =  C2)  side.  Then,  if  Xrand  Cr  are  the  respective  values  of 
X  and  C  at  resonance,  i.e.,  when  the  dynamometer  effect  is  zero,  we  have: 

,  7  Xi    —   Xr  _.       Xr  X2  Xi  X2 

d\  +  d2  =  2w  —  r—  -  =  2ir  —  r  --  =  approx.  IT  —  — 

Xi  X2  Xr 

Ci  -Cr  C,—  C,  7T  Cl  -  C2 


With  this  method  it  is  not  necessary  to  determine  the  entire  resonance 
curve.  However,  for  most  purposes  the  method  is  sufficiently  accurate, 
as  it  is  relatively  easy  to  sharply  locate  a  maximum  and  as  the  absolute 
value  of  the  deflection  at  the  maximum  has  no  bearing  upon  the  results.  • 

6.  If  great  accuracy  is  of  importance,  the  method  based  on  Art.  80d2 
should  be  employed.  The  resonance  curve  is  plotted  with  either  the 
wave-lengths  or  capacities  of  the  measuring  circuit  as  abscissae.  Then  a 
line  is  drawn  parallel  to  the  axis  of  abscissae  and  intersecting  the  curve  at 
two  points  whose  abscissae  are  X'  and  X"  or  C'  and  C"  respectively.  Then 
if  \r  and  Cr  are  the  resonance  values,  we  have  : 


C"    -Cr         C"   -Cr 


83.  The  Dynamometer.  —  Modified  forms  of  the  ordinary  dynamome- 
ters may  be  used  for  measuring  the  dynamometer  effect,  a  fixed  and  a 
movable  coil,  the  latter  suspended  on  a  bronze  strip  and  provided  with  a 


136 


WIRELESS  TELEGRAPHY 


mirror  similarly  to  the  coils  of  a  Deprez-d'Arsonval  mirror  type  instru- 
ment.    Both  coils  must  have  only  a  small  number  of  turns.131 

A  "short-circuit  loop  dyna- 
mometer" (MANDELSTAM  and  PAPA- 
LExi129)  has  given  very  good  results. 
a.  Its  construction,  for  labora- 
tory purposes  is  shown  in  Fig.  170, 
its  diagrammatic  connections  in 
Fig.  171.  There  are  two  flat  coils, 
Si  and  82,  perpendicular  to  each 
other  and  between  the  two,  but 
coaxial  with  $2  an  aluminium  loop 
or  ring  with  a  small  mirror  is  sus- 
pended on  a  fine  thread.  The  two 
currents  I'i  and  7'2  of  Fig.  169  are 
sent  through  the  coils  Si  and  $2  in 
order  to  measure  their  dynamome- 
ter effect.  The  resulting  action  is 
as  follows:  The  current  7'2,  sent 
through  $2  induces  a  current  73,  in 
the  loop,  which  is  in  phase  with  7'2 
and  proportional  in  amplitude  to 
If2,  on  condition  that  the  inductance 
of  the  loop  is  greatly  in  excess  of 
its  resistance.132  The  current  in  /S2 
causes  no  turning  force  to  act  on 
the  loop,  as  $2  and  the  loop  are 
coaxial.  But  the  current  I'\  pass- 
ing through  Si  induces  no  current  in  the  loop  as  their  planes  are  perpen- 
dicular to  each  other;  it  does,  however,  produce  a  torque  upon  the  loop 
proportional  to  the  dynamometer  effect  I\I3  and  hence 
also  ex  JVV 

This  is  true  accurately  only  at  the  zero  position  of 
the  loop.  Careful  analysis  of  the  conditions,  however, 129 
has  shown  that  even  when  the  loop  has  been  turned 
from  its  position  of  rest  through  a  small  angle,  its  de- 
flection oc  I'J'i.  With  the  arrangement  of  Fig.  169,  the 
deflection  is 


FIG.  170. 


a . 


FIG.  171. 


in  which  b  is  the  torsion  moment  of  the  suspension  system,  f  is  the  number 
of  discharges_per  second  and  a  and  c  are  the  constants  of  the  apparatus. 
Hence  #  oc  F 


RESONANCE  CURVES  137 

b.  If  the  torsion  moment  of  the  suspension  system  is  made  very  small 
(quartz  thread),  the  factor  b  in  the  equation  of  paragraph  a  becomes  very 
small  in  comparison  to  f  .  c7'2ie//.  Then  we  have 


i.e.,  5  becomes  independent  of  the  discharge  frequency,  f,  and  thereby 
independent  of  the  more  or  less  irregular  operation  of  the  interrupter,  if 
an  induction  coil  or  interrupted  direct  current  is  used. 

3.  USE  OF  RESONANCE  IN  THE  STUDY  OF  CONDENSERS 

84.  Determination  of  the  Frequency  Factor. — The  following  will  serve 
as  a  simple  arrangement.  Construct  a  primary  circuit  (condenser  circuit 
/,  Fig.  172),  having  that  frequency  at  which  the  frequency  factor  of  the 


FIG.  172. 

condenser  is  to  be  determined.  Connect  the  test  condenser,  (7,  into  a 
circuit  containing  a  variable  self-inductance,  S,  by  means  of  which  this 
condenser  circuit,  77,  is  brought  into  resonance  with  the  primary  circuit, 
7.  Then  replace  C  by  a  calibrated  adjustable  air  condenser  and  vary  its 
capacity  until  circuit  77  is  again  in  resonance  with  the  primary.  Then  the 
capacity,  C,  of  the  test  condenser  is  equal  to  that  of  the  air  condenser  at 
resonance.  Now  find  the  capacity,  C8,  of  the  test  condenser  for  static 
charges  (see  foot-note,  Art.  72o).  Then  [Art.  5a],  the  frequency  factor 
for  the  frequency  in  question  is 

f.c_ 

3  "  c, 

This  method  is  easily  modified  in  numerous  ways  to  adapt  itself  to  any 
given  case.  The  only  essential  feature  is  the  replacing  of  the  unknown 
capacity  by  that  of  an  air  condenser  (which  is  independent  of  the  fre- 
quency [Art.  5a])  and  maintaining  resonance. 


138  WIRELESS  TELEGRAPHY 

In  applying  this  method  it  is  important  to  choose  the  coefficient  of  self- 
induction  of  circuit  II  so  that  the  frequency  will  not  be  appreciably 
affected  by  the  currents  in  the  condenser  coatings  or  by  such  slight  changes 
in  the  leads  to  the  condenser  as  may  be  necessary  in  view  of  the  different 
construction  of  the  air  condenser  and  the  various  test  condensers. 

If  it  is  desired  to  compare  the  frequency  factors  of  a  number  of  con- 
densers having  different  dielectrics,  the  same  electric  field  strength  in  the 
dielectric  should  be  used  in  each  case,  as  this  may  affect  the  frequency 
factor. 

85.  Energy    Absorbed    by    Dielectric  Hysteresis.21 — a.  The    same 
arrangement  as  that  of  Fig.  172  applies.     Assume  the  secondary  circuit, 
//,  which  includes  the  test  condenser,  to  be  in  resonance  with  the  primary 
circuit  and  that  the  deflection  of  the  measuring  instrument  in  the  indi- 
cating circuit  is  a'.     The  condenser,  C,  is  then  replaced  by  a  variable  air 
condenser  which  is  adjusted  until  resonance  is  again  obtained.     Let  a  be 
the  instrument  deflection  which  now  results.     Then  from  these  values  and 
equation  (2)  Art.  76,  we  obtain  the  increase,  d',  in  the  decrement  of  the 
secondary  circuit  caused  by  the  energy  absorption  in  the  condenser  C  and 
which   characterizes   the   energy   absorption   of  the   particular   dielectric 
material  [Art.  13]. 

b.  For  comparing  various  condensers  it  may  be  simpler  to  determine 
their  equivalent  resistance  [Art.  776]  by  substitution.     For  this  purpose, 
after  having  replaced  C  (Fig.  172)  by  an  air  condenser  and  readjusted  for 
resonance,  sufficient  resistance  is  connected  into  the  secondary  until  the 
instrument  deflection  is  again  a'.     This  resistance,  R',  is  the  equivalent 
resistance  of  the  condenser.133 

c.  In  applying  this  method,  which  may  be  modified  in  various  ways,  it 
is  especially  important  to  avoid  eddy  currents  in  the  condenser  coatings. 
Their  effect  can  entirely  destroy  the  accuracy  of  the  results.     In  con- 
densers in  the  form  of  Ley.den  jars  it  is  quite  difficult  to  avoid  eddy 
currents,  or  even  to  determine  whether  the  eddy  currents  have  been 
eliminated.     A  convenient  safeguard,  applicable  only  to  plate  condensers, 
however,  is  to  place  the  condensers  in  various  positions  or  to  use  first  zinc 
sheet  electrodes  and  then  copper  electrodes.     If  this  causes  no  change  in 
the  instrument  deflection  it  may  generally  be  concluded  that  the  existing 
eddy  currents  are  negligible. 

d.  In  comparing  the  energy  absorption  of  different  materials  it  is  also 
important  to  use  the  same  electric  field  intensity  throughout  in  the  dielec- 
tric, as  this  may  affect  the  result.     Similarly  only  values  obtained  at  the 
same  frequency  should  be  compared. 

86.  The   Brush   Discharge   of   Condensers    (W.    EiCKHOFF134). — a. 
Curve  a  in  Fig.  173  is  the  resonance  curve  of  a  condenser  circuit  whose 
condensers  have  no  brush  discharge;  curve  b  was  obtained  with  the  same 


RESONANCE  CURVES 


139 


circuit  but  with  a  heavy  brush  discharge  from  the  condensers  [Art.  14a]. 
The  difference  between  the  two  curves  is  twofold,  viz., 

1.  b  is  not  symmetrical,  falling  off  much  more  rapidly  on  the  side  of  the 
higher  frequencies,  while  curve  a  is  symmetrical. 

2.  The  resonance  point  (maximum  current  effect)  in  b  occurs  at  a  lower 
frequency  (greater  wave-length)  than  in  a. 

Both  these  points  are  characteristic  of  condensers  with  brush  discharge. 

b.  The  explanation  of  this  phenomenon  is  to  be  found  in  the  following: 
The  brush  discharge,  by  charging  the  uncoated  portion  of  the  con- 
denser, causes  an  increase  in  its  capacity  and  a  decrease  in  the  natural  fre- 
quency of  the  circuit.     The  effect,  however,  is  not  the  same  as  when 
another  second  condenser  is  joined  in  parallel  to  the  coatings  of  the  first 
through  a  metallic  connection, 

for  the  conducting  path  be- 
tween the  coated  and  un- 
coated portions  really  consists 
of  the  brush  discharge  itself, 
which  jumps  from  point  to 
point  very  irregularly.  Hence 
the  amount  of  the  charge 
held  on  the  uncoated  portion 
of  the  condenser  is  also  con- 
tinuously fluctuating.  The 
irregularity  of  this  parasitic  FIG.  173. 

capacity    and    its    connection 

to  the  coated  condenser  will  result  in  a  varying  frequency  whose  maxi- 
mum value  is  determined  by  the  capacity  of  the  coated  portion.* 

Hence,  if  such  a  condenser  circuit  is  caused  to  act  upon  a  resonance 
circuit  and  if  the  frequency  of  the  latter  is  gradually  decreased,  the  cur- 
rent effect  will  rise  with  relative  rapidity  as  soon  as  the  maximum  fre- 
quency just  mentioned  is  approached.  It  will,  however,  retain  compara- 
tively great  values  as  long  as  the  frequency  of  the  resonance  circuit 
remains  in  the  range  of  the  frequency  fluctuations  caused  by  the  brush 
discharge  in  the  primary  circuit.  The  result  therefore  is  a  widening 
of  the  resonance  curve  in  the  direction  of  the  lower  frequencies. 

c.  The  widening  of  the  resonance  curve  indicates  a  considerable  reduc- 
tion in  the  resonance  sharpness;^  it  is  caused  mainly  by  the  fluctuations  in 
the  frequency,  as  was  shown  in  the  preceding  paragraphs. 

Hence  the  amount  of  the  energy  loss  due  to  the  discharge  can  not  be 

*  In  all  probability,  these  fluctuations  in  the  frequency  are  accompanied  by  varia- 
tions in  the  initial  amplitude  and  irregularities  in  the  fall  of  the  amplitude  during 
each  oscillation. 

f  The  resonance  sharpness  is  about  24  for  curve  a  and  about  10.5  for  curve 
6  in  Fig.  173. 


140 


WIRELESS  TELEGRAPHY 


determined  [Art.  78a]  from  the  resonance  curves  which  give  only  an  upper 
limit  for  the  loss. 

If  the  value  di  +  d%  is  obtained  from  the  resonance  curves  by  applying 
the  relations  of  Art.  74,  there  being  no  brush  discharge  on  the  condensers, 
and  the  value  d'i  +  d2  is  obtained  with  a  brush  discharge  on  the  con- 
densers, other  conditions  being  the  same,  then  the  increase  in  the  decre- 
ment due  to  the  brush  discharge  can  not  be  more  than  (d\  +  d2)  —  (di  + 

&)  =  d\  -  d,. 

However,  the  resonance 
curves  may  also  be  used  for 
obtaining  a  quantitative  value 
of  the  effect  of  the  brush  dis- 
charge on  the  sharpness  of 
resonance.  The  equations  of 
Art.  74  are  applied  to  the 
curve  and  di  +  d%  is  deter- 
mined. Subtracting  from  this 
the  decrement  of  the  measur- 
ing circuit,  d2,  we  have  d\, 
which  may  be  considered  as 
being  the  decrement  of  a 
condenser  circuit  having  no 
brush  discharge  but  having 
the  same  resonance  sharp- 
ness. * 

The  result  of  measurements  made  in  this  way  (W.  EiCKHOFF134)  is 
shown  in  Fig.  174  for  Ley  den  jars  of  German  flint  glass,  f  The  three 
full-line  curves  show  the  relation  of  di  to  the  potential  amplitude,  first 
with  the  capacity  consisting  of  a  single  Ley  den  jar,{  then  with  2X2 
Leyden  jarsj  connected  as  in  Fig.  12,  and  lastly  with  3X3  jars,J  con- 
nected as  in  Fig.  13,  the  outer  circuit  remaining  the  same  for  each  case. 
In  the  first  case  the  entire  potential  difference  exists  between  the  con- 

*  The  actual  reduction  in  amplitude  caused  by  the  brush  discharge  does  not 
come  into  question. 

f  M.  WiEN17  has  found  the  following  apparent  increase  in  the  decrement  due  to 
brush  discharge: 


I 

08  - 

$_ 

1 

, 

( 

1  

f,^ 

_i 

fl 

|: 

02 

g 

/ 

/ 

^ 

, 

/  Wf 

/ 

f  ^ 

''  sVr' 

0.1  - 

"1"~ 

*** 

*=  = 

=  r? 

'** 

5 

"" 

•  o  . 

«,_    Single 

Jar  under  Oi 

"H 

10s  Volt-*     10          20 

SO         40          50          60          70 

Spark  Length  35          8          12    15     20         SO  34 
in  mm 
FIG.  174. 

Potential  amplitude 

0.9  X  104  volts 
1.55  X  104  volts 
2.2  X  104  volts 


Leyden  jars  of  English 
flint  glass 

0.008 
0.028 
0.064 


Jars  made  by 
H.  Boas. 

0.002 
0.002 

0.007 


J  All  the  jars  had  practically  the  same  capacity,  so  that  the   resultant  capacity 
in  the  various  combinations  remained  just  about  the  same. 


RESONANCE  CURVES  141 

denser  coatings;  in  the  second  case  only  one-half;  in  the  last  case  only 
one-third.  The  brush  discharge  is  accordingly  greatest  in  the  first  and 
least  in  the  third  case. 

The  uppermost  curve  shows  how  very  detrimental  the  effect  of  brush 
discharge  may  be  to  the  resonance  sharpness.  A  comparison  of  the 
three  curves  shows  that  this  harmful  effect  may  be  combatted  by 
series-parallel  combinations  of  the  condensers  [Art.  4d], 

As  a  matter  of  fact,  such  series-parallel  combinations  of  equal  con- 
densers can  produce  the  desired  result  only  if  the  apparent  increase  in  the 
decrement  due  to  brush  discharge  with  increasing  potential  varies  more 
rapidly  than  TV.  If  it  °c  Fo2,  a  simple  consideration  will  make  it  evident 
that  nothing  is  gained  (L.  W.  AUSTIN  21)  by  series-parallel  combinations. 
Above  what  potential  the  apparent  decrement  increase  rises  more  rapidly 
than  F02  depends  upon  the  form  and  material  of  the  condensers. 

d.  As  these  series-parallel  connections  involve  considerable  compli- 
cation, it  is  desirable  to  overcome  brush  discharge  in  some  simpler  way. 
This  may  be  accomplished  by  placing  the  condensers,  or  at  least  the  edges 
of  their  coatings,  in  a  heavy  oil.     The  extent  to  which  this  can  reduce  the 
detrimental  effect  of  brush  discharge  is  shown  by  the  dotted  curve  in 
Fig.  174. 

However,  this  is  a  dangerous  method.  For,  if  the  voltages  are  not 
comparatively  low,*  the  condensers  are  almost  certain  to  break  down. 
Bad  as  a  brush  discharge  may  be  it  has  one  good  feature  about  it,  namely, 
a  certain  protection  against  breaking  down  of  the  condensers. 

e.  From  the  preceding,  we  may  draw  certain  conclusions  of  practical 
importance,  viz., 

1.  Displacement  of  the  point  of  resonance  [a2],  other  things  being 
equal,  ^increases  together  with  the  potential  amplitude,  in  fact  is  pro- 
portional to  it  under  the  conditions  applying  to  such  investigations  as 
have  been  made.     Hence,  as  brush  discharge  can  not  be  entirely  over- 
come in  primary  circuits,  the  tuning  between  primary  and  secondary 
must  be  done  at  the  same  potential  at  which  the  circuits  will  be  used 
later. 

2.  The  influence  of  brush  discharge  in  cylindrical  condensers  becomes 
less  according  as  the  diameter  is  made  smaller  in  comparison  to  the 
length,  other  things  remaining  equal,  as  this  makes  the  parasitic  capacity 
smaller  in  proportion  to  the  normal  capacity.     Hence,  from  this  point  of 
view  it  is  better  to  use  long,  narrow  than  short,  wide  jars. 

3.  Thickening  the  uncoated  end  of  the   condensers   (Leyden  jars) 
also  reduces  the  parasitic  capacity  and  the  effect  of  the  brush  discharge 
(see  Art.  396). 

*  With  the  best  flint  glass,  5  mm.  in  thickness,  30,000  volts  (corresponding  to 
1  cm.  gap)  is  the  extreme  limit. 


142 


WIRELESS  TELEGRAPHY 


4.  THE  USE  OF  RESONANCE  CURVES  FOR  INVESTIGATING  COUPLED 

CIRCUITS 

(J.  ZENNECK/  C.  FISCHER, 90  M.  WiEN90) 

87.  Coupling  of  Tuned  Circuits. — Determination  of  Frequency,  Dec- 
rement and  Degree  of  Coupling. — If  the  oscillations  of  coupled,  tuned 
circuits  [Art.  55,  et  seq.]  are  caused  to  act  upon  a  measuring  circuit,  reso- 
nance curves  of  the  form  shown  in  Fig.  175  will  be  obtained,  if  the  cir- 
cuits are  quite  closely  coupled.  The  relations  of  Arts.  71  and  74  may  be 
applied  to  both  of  the  parts  of  these  curves.  The  location  of  the  two 
peaks  gives  the  values  of  the  frequencies  N1  and  N11  (and  the  wave-lengths 
X1  and  X77)  of  the  two  oscillations,  the  form  of  the  curve  around  the 
two  peaks  gives  the  decrements  d1  and  d11  and  the  degree  of  coupling 
[Art.  95]  is 


2.2         2.4         2.6        2.8          3          3.2        3.4Xl06/Sec 
Frequency  of  the  Measuring  Circuit 

FIG.  175. 


1  - 


Kf  = 


1  + 


in  which  N  and  X  are  the  frequency  and  wave-length  respectively  of  both 
circuits  before  coupling.*  If  the  coupling  is  not  very  close  this  may  be 
simplified  into 

X"-X' 

~~ 


Table  X  gives  the  values  of  K'  for  different  ratios  of  the  frequencies. 
With  loose  coupling,  however,  the  resonance  curves  assume  the  shape 

*  If  C1,  C77  and  C  represent  the  capacities  of  the  measuring  circuit  corresponding 
to  the  wave-lengths  X7  X77  and  X,  then  K'  =  ^ ~ — 


RESONANCE  CURVES 


143 


of  the  full-line  curve  in  Fig.  176.  The  two  peaks  do  not,  in  general,  occur 
at  the  points  corresponding  to  the  two  frequencies.  Hence  N1  and  N11 
(as  well  asX1  andX11)  cannot  be  determined  from  the  location  of  the  peaks, 
nor  can  the  decrements  be  found  by  applying  the  methods  of  Art.  74. 
In  this  case  we  must  proceed  as  follows.136 

a.  The  method  in  this  case  is  based  on  the  fact  stated  in  Art.  616 
that  of  the  oscillations  of  the  same  frequency 

7 11  j  are  approximately  in         Ii11  1  are  displaced  approxi- 
727  j      phase.  7/J  j      mately  180°. 

This  relation  makes  it  possible  to  practically  eliminate  the  effect  of  one 
of  the  pairs  upon  the  measuring  circuit,  subjecting  the  latter  only  to  the 
other  pair. 


Tl 

ww 

uuuuu 

LF 

FIG.  177. 

2.2         2.2b        N  2.32 

Frequency  of  the  Measuring  Circuit 

FIG.  176. 


b.  The  arrangement  is  shown  diagrammatically  in  Fig.  177.  Small 
wire  loops,  KI  and  K2,  are  connected  into  the  primary  and  secondary 
circuits  respectively,  and  similar  loops,  MI  and  M2,  are  joined  to  the 
measuring  circuit  (777) .  KI  acts  inductively  only  upon  MI,  K2  only  upon 
M2. 

The  phase  relations  of  the  electromotive  forces,  E,  are  the  same  as  for 
the  corresponding  currents,  and  we  have  approximately 

Ei1  ]  E  H  ' 

^//  [   in  phase,  ^u  \  displaced  180°.     We  will  assume  that  these  rela- 
tions instead  of  being  only  approximate  are  exact. 

The  amplitude  of  these  electromotive  forces,  aside  from  depending 
on  the  currents  7/,  727,  etc.,  also  depend  on  the  distances  between  KiMi 
and  KzMz.  If  these  distances  are  adjusted  until  the  amplitudes  of  Ei1 
and  E2H  are  equal,  then  Ei1  and  E2n  will  neutralize  each  other. 


144  WIRELESS  TELEGRAPHY 

The  result  is  that  oscillation  II  (frequency  N77)  has  absolutely  no  effect 
upon  the  measuring  circuit,  which  acts  as  if  only  the  oscillation  of  fre- 
quency N1  and  decrement  d1  existed.  Hence  if  the  resonance  curve  is 
plotted  in  this  way,  it  will  represent  only  this  one  oscillation,  and  N1  or 
X7  and  d1  can  be  obtained  from  it  in  the  usual  way. 

To  obtain  the  opposite  effect,  that  is,  obviate  oscillation  /  so  that 
only  oscillation  II  will  be  measured,  all  that  is  necessary  is  to  revolve  the 
loop  MI  (or  else  MZ)  through  180°  and  then  proceed  just  as  before;  EI 
and  EZ   now  neutralize  each  other  while  Ei1  and  E%n  are  added  to  each 
other. 

c.  The  method  of  procedure  therefore  is  as  follows.     First  a  resonance 
curve  is  plotted,  having,  in  general,  two  maxima.     Then  the  distance 
between  MI  and  KI  (or  M%  and  Kz)  is  varied  until  only  one  maximum 
remains  in  the  resonance  curve,  all  indications  of  the  second  peak  having 
disappeared;  the  curve  is  then  the  resonance  curve  of  one  oscillation. 
Then  M i  is  turned  through  180°.     If  a  trace  of  the  former  maximum 
remains,  it  should  be  eliminated  by  a  final  adjustment  of  the  distance 
between  MI  and  KI  (or  MZ  and  Kz).     The  curve  then  is  the  resonance 
curve  of  the  second  oscillation. 

The  dash  and  dot-and-dash  curves  of  Fig.  176  were  obtained- in  this 
way.  They  are  the  resonance  curves  of  the  two  oscillations;  from  them 
may  be  obtained  the  frequencies  N1  and  N11)  the  decrements  d1  and  d11 
and  the  degree  of  coupling  K' '. 

d.  In  the  practical  application,  the  loops  KI  and  KZ  may  be  entirely 
omitted,  the  primary  and  secondary  circuits  being  used  in  their  normal 
form  to  act  upon  M  i  and  MZ.     The  latter,  however,  i.e.,  loops  M  i  and  MZ, 
are  best  retained,  as  they  simplify  the  manipulation.     The  following 
points  should  also  be  noted: 

1.  Moving  MI  (or  MZ)  must  not  change  the  self-induction  of  the 
measuring  circuit.     This  is  provided  for  by  placing  the  leads  connecting 
these  loops  to  the  rest  of  the  circuit  of  wires  very  close  together. 

2.  For  precise  measurements  it  is  important  to  entirely  eliminate  the 
effect  of  the  oscillation  other  than  the  one  whose  resonance  curve  is  being 
determined.     This  can  be  done  as  follows:  Assume  oscillation  //  is  to 
be  eliminated,  after  an  approximate  value  of  N11  has  been  obtained  as 
described  above.     The  measuring  circuit  is  adjusted  to  have  this  fre- 
quency N11.     Then  the  loops  MI  and  KI  are  adjusted  with  respect  to 
their  relative  position,  until  the  electromotive  forces  E-f1  and  Ez11  are 
added  and  the  current  effect  in  the  measuring  circuit  becomes  as  great  as 
possible.     Only  then  is  MI  turned  through   180°;  this  procedure  will 
result  in  a  much  more  complete  elimination  of  oscillation  II  than  before.  * 

*The  necessity  for  this  precaution  is  due  largely  to  the  fact  that  the  deflections 
of  the  measuring  instruments  which  can  be  used  for  this  purpose  depend  upon  the 
mean  square  of  the  current  value.  Even  when  the  effect  of  oscillation  II  is  not 


RESONANCE  CURVES 


145 


e.  The  accuracy  of  this  method  is  very  high  so  far  as  determinations 
of  frequency  and  degree  of  coupling  are  concerned.  But  in  view  of  the 
assumption  made  in  b  not  being  strictly  correct,  the  values  of  the  decre- 
ments d1  and  d11  found  in  this  way  may  involve  considerable  errors, 
the  extent  of  which  can  hardly  be  fixed  in  each  case  (B.  MACKU138). 

88.  Close  Coupling  of  Tuned  Circuits.  Current  Effect  in  a  Third 
Circuit.90 — Consider  a  secondary  circuit  tuned  to  and  closely  coupled  to  its 
primary  and  at  the  same  time  very  loosely  coupled  to  a  third  (measuring) 
circuit.  Two  questions  present  themselves,  viz., 

1.  How    does    the    total    current 
effect    in    the    third    circuit    depend 
upon  the  latter's  frequency? 

2.  If    the   third   circuit   is   synto- 
nized with  one'  of  the  oscillations  of 


II 


\a 


0.5 


K 


0.4 


FIG.  178. 


FIG.  179. 


the  secondary  circuit,  how  does  the  current  effect  in  the  third  circuit  de- 
pend on  the  coupling  between  the  primary  and  secondary  circuits? 

a.  The  answer  to  the  first  question  follows  directly  from  Art.  87.  The 
heavy  full-line  curve  of  Fig.  176  shows  how  the  current  effect  in  the  third 
circuit  depends  on  the  natural  frequency  of  this  circuit.  Comparison  with 
the  dash  and  dot-and-dash  lines  (the  resonance  curves  of  the  individual 
primary  and  secondary  oscillations)  shows  that  the  maximum  current 
effect  in  the  third  circuit  does  not  occur  when  it  has  the  same  frequency  as 
one  of  the  oscillations  in  the  secondary  circuit.  The  maximum  for  the 
slower  oscillation  occurs  at  a  somewhat  lower  frequency,  that  of  the  more 
rapid  oscillation  at  a  higher  frequency. 

The  curves  of  Fig.  176  represent  quite  a  loose  coupling  (Kr  =  0.028). 

sufficient  to  show  signs  of  a  second  maximum  in  the  lower  portion  of  the  resonance 
curve  of  oscillation  7,  it  may  nevertheless  greatly  influence  the  shape  of  the  upper 
part  of  the  curve. 
10 


146 


WIRELESS  TELEGRAPHY 


The  closer  the  coupling  becomes  the  more  nearly  do  the  maxima  of  the 
current  effect  in  the  third  circuit  coincide  with  the  frequencies  N1  and 
N11  of  the  oscillations  in  the  secondary  circuit. 

6.  The  curves  in  Figs.  178,  179  and  180*  show  the  relation  of  the  cur- 
rent effect  in  the  third  circuit  to  the  percentage  of  coupling,  first  with  the 
third  circuit  tuned  to  the  more  rapid  oscillation  (7),  then  to  the  slower 
oscillation  (77).  These  curves  show: 

1.  In  all  cases  there  is  a  very  decided  maximum  current  effect  for  both 
oscillations,  always  occurring  at  a  relatively 

very  low  frequency.  The  less  the  damping 
of  the  secondary  and  tertiary  circuits,  the 
more  decided  is  the  maximum. 

2.  Up  to  this  maximum  there  is  no  notice- 
able difference  between  the  more  rapid  (7)  and 


b— 


FIG.  180. 


0.1         0.2         0.3 

>- 

FIG.  181. 


the  slower  (77)  oscillation.  But  as  the  coupling  is  increased  beyond  the 
maximum,  the  oscillation  of  the  higher  frequency  (7)  may  produce  a 
considerably  greater  current  effect  than  the  slower  oscillation. 

The  curves  of  Figs.  178,  179  and  180  were  all  obtained  with  primary 
circuits  having  a  spark  gap.  The  conclusion  (2)  just  drawn  from  the 
curves  would  in  fact  not  apply  otherwise.  If  the  primary  circuit  has  no 

*  Fig.  178:  Ci  =  C2  =  0.85  X  W~3MF.     L,  =  L2  =  22,000  cm.;  di  =  0.11 
a:  d2  =  0.14  6:  d2  =  0.20 

d3  =  0.10 

Figs.  179  and  180:  Ci  =  5.29  X  10~3M^. 
C2  =  0.45  X  W~*MF. 
Fig.  179a:  d*  =0.034 
d3  =  0.031 
Fig.  180c:  d2  =  0.21 
d3  =  0.20 

Fig.  181:  The  letters  correspond  to  the  same  conditions  as  in  Figs.  179  and  180. 
Length  of  primary  spark  gap  about  6  mm. 


d3  =  0.20 

=    6,230  cm.   \   ,    _  n  IK 
=  73,000  cm.   /  * 
Fig.  1796:  d2  =0.10 

d3  =  0.10 
Fig.  180d:  d2  =  0.37 

d3  =  0.31 


RESONANCE  CURVES  147 

spark  gap,  theory90  shows  that  the  current  effect  must  be  the  same  for  both 
oscillations. 

c.  It  may  at  times  be  interesting  to  compare  the  current  effect  in  a 
third  circuit  tuned  to  one  of  the  coupling  oscillations  with  the  total  current 
effect  in  the  secondary  circuit.  The  latter's  variation  with  the  coupling  is 
shown  in  Fig.  181  for  the  same  circuits  referred  to  by  Figs.  178,  179  and 
180. 

The  use  of  very  short  spark  gaps  (less  than  1  mm.)  alters  these  condi- 
tions materially.  In  this  case,  as  the  percentage  of  coupling  is  gradually 
increased,  the  current  effect  in  the  secondary  circuit  may  pass  through  a 
succession  of  maxima  and  minima.  Careful  investigation  has  shown  that 
the  maxima  are  due  to  particularly  thorough  quenching,  the  minima  to 
particularly  poor  quenching  in  the  gap  of  the  primary  circuit  (H. 

RlEGGER).7 

With  thorough  quenching  in  the  primary  gap,  the  current  effect  in  the 
secondary  may,  under  certain  conditions,  be  greatest  when  the  primary 
quenched  gap  circuit  is  slightly  out  of  resonance  with  the  secondary 
circuit.139  This,  however,  is  by  no  means  universally  the  case;  in  many 
arrangements  bringing  the  circuits  out  of  resonance  does  not  in  the  least 
increase  the  current  effect  obtained  at  precise  resonance  in  the  secondary. 

89.  Coupling  Untuned  Circuits.  Current  Effect  in  a  Third  Circuit 
(M.  WiEN90'92). — Conditions  are  somewhat  altered  if  the  primary  and 
secondary  circuits  have  slightly  different  frequencies  before  being  coupled, 
that  is,  are  slightly  out  of  resonance. 

a.  Theoretical  investigation  has  led  to  the  following  conclusions  for 
circuits  without  spark  gaps.  If  the  decrements  di  and  d2  of  the  primary 
and  secondary  circuits  are  different  before  coupling,  it  is  possible,  by 
bringing  the  two  circuits  out  of  resonance,  to  obtain  a  current  effect  in 
one  of  the  two  oscillations  which  is  greater  than  when  the  primary  and 
secondary  are  exactly  in  tune. 

1.  If  di<d2,  we  have  two  possibilities,  viz.,  either  the  current  effect 
of  the  more  rapid  oscillation  (7)  is  increased  when  the  primary  has  a 
higher  frequency  than  the  secondary,  or  the  current  effect  of  the  slower 
oscillation  (//)  is  increased  when  the  secondary  has  the  higher  frequency. 

2.  If  di>d2,  what  has  just  been  stated  for  the  more  rapid  oscillation, 
holds  for  the  slower  and  vice  versa. 

The  increase  in  the  current  effect  is  greatest  for  a  certain  dissonance. 
This  amount  of  dissonance,  other  things  being  equal,  increases  as  the 
difference  between  di  and  d2  increases  and  as  the  coupling  is  made  closer. 
In  general  only  about  20  per  cent,  increase  in  the  current  effect  is  the  most 
that  can  be  obtained. 

6.  With  a  spark  gap  in  the  primary  circuit  the  relations,  so  far  as  can 
be  concluded  from  such  investigations  as  have  been  made  to  date,  are 
qualitatively  the  same.  But  in  general  the  strengthening  of  the  current 


148 


WIRELESS  TELEGRAPHY 


effect  is  not  quite  so  great  as  for  primary  circuits  without  a  spark  gap  and 
under  certain  conditions  the  more  rapid  oscillation  (7)  seems  to  be  the 
most  favored. 

90.  Investigation  of  the  Quenching  Action  in  Spark  Gaps. — The  reso- 
nance curves  of  the  current  effect  given  in  §1  are  especially  well  adapted 
for  studying  the  action  of  quenched  gap  circuits.  For  this  purpose  the 
secondary  circuit  coupled  to  the  quenched  gap  circuit,  is  in  turn  coupled 
very  loosely  with  a  measuring  circuit  (Fig.  152)  and  the  resonance 
curve  of  the  current  effect  is  plotted  in  this  way. 

a.  If  the  resulting  curve  has  the  form  of  curve  b  in  Fig.  182,  the  coup- 
ling oscillations  are  present  and  there  is  no  quenching  action.  If,  however, 

the  result  is  like  curve  a  of  Fig. 
182,  this  indicates  complete 
quenching  and  only  the  natural 
oscillations  of  the  secondary  cir- 
cuit are  present.  A  resonance 
curve  formed  like  curve  C  of 
Fig.  182  shows  that  in  addition 
to  the  natural  oscillations  of  the 
secondary,  the  coupling  oscilla- 
tions are  also  present. 

This  may  be  due  to  any  of 
three  causes.  Either  the  coup- 
ling oscillations  occur  at  one 
discharge,  and  quenching  occurs 
at  another.  Or  the  oscillations 
in  the  secondary  circuit  are 
always  of  the  same  kind,  but  the 
quenching  action  is  not  complete,  " impure,"  i.e.,  the  primary  oscillations 
are  not  quenched  until  more  than  half  an  oscillation  is  completed  [Art. 
64a].  These  two  cases  can  be  distinguished  by  coupling  the  secondary 
very  loosely  with  a  resonance  circuit  tuned  to  the  natural  frequency  of  the 
secondary  circuit.  A  small  spark  gap  is  connected  in  parallel  with  the 
condenser  in  the  resonance  circuit  .and  adjusted  so  as  to  respond  regu- 
larly. This  small  gap  is  then  placed  alongside  of  the  main  quenched  gap 
in  the  primary  and  both  are  observed  in  a  rotating  mirror.  If  the 
quenched  spark  gap  is  seen  in  the  mirror  first  alone  and  then  together 
with  the  small  gap  and  so  on,  we  evidently  have  the  first  case  (H. 

RlEGGER140). 

The  third  possibility  is  the  existence  of  a  thorough  quenching  action, 
but  a  very  loose  coupling.  Then  the  duration  of  half  an  oscillation  and 
hence  the  time  during  which  two  coupling  oscillations  exist  together 
[see  foot-note  to  Art.  78c]  is  so  great  that  the  latter  become  apparent  in 
the  resonance  curve. 


O 
FIG.  182. 


RESONANCE  CURVES  149 

b.  From  Art.  64  it  follows  that  such  observations  as  have  just  been 
described  in  a,  offer  a  direct  means  of  answering  the  question  of  the 
critical  degree  of  coupling  so  important  in  practice,  and  thereby  also  the 
question  of  which  of  two  spark  gaps  has  the  better  quenching  action. 
The  coupling  is  made  closer  and  closer;  the  critical  and  therefore  the 
best  degree  of  coupling  is  that  at  which  the  coupling  oscillations  have  not 
yet  appeared  but  are  just  about  to  become  noticeable  in  the  resonance 
curve. 

It  was  stated  in  Art.  646  that,  under  certain  conditions,  several 
critical  degrees  of  coupling,  at  which  complete  quenching  is  obtained,  may 
be  found.  In  such  cases  a  comparison  of  various  gaps  as  to  their  quench- 
ing action  is  very  difficult. 

c.  The  resonance  curve  also  offers  a  simple  means  of  determining 
whether  a  given  method  of  increasing  the  quenching  action  (e.g.,  air 
blowers,  magnetic  blow-outs,  the  use  of  hydrogen  instead  of  air,  etc.),  is 
really  effective141).     First  a  condition  of  impure  quenching,  in  which  the 
coupling  oscillations  are  evident  in  the  resonance  curve  in  addition  to  the 
natural  oscillation  of  the  secondary  circuit  (curve  c  .of  Fig.  182)  is  inten- 
tionally obtained.     If  then  application  of  the  method  to  be  tested  causes 
the  indications  of  the  coupling  oscillations  to  disappear  from  the  reso- 
nance curve,  this  is  proof  of  an  improved  quenching  action. 


CHAPTER  VI 
THE  ANTENNA 

91.  General. — Just   as   in   ordinary   wire   telegraphy,    so   in   radio- 
telegraphy,  a  system  of  communication  is  essentially  comprised  of  two 
stations,  viz.,  the  "transmitting"  and  the  "receiving"  station.     Similarly, 
the  collection  of  apparatus  used  for  sending  off  telegrams  is  called  the 
"transmitter"  or  "transmitting  set,"  while  the  corresponding  apparatus 
at  the  receiving  station  is  termed  the  "receiver"  or  "receiving  set." 

Every  radio  station  has  an  open  oscillator,  the  "antenna,"  that  part 
of  the  antenna  which  is  suspended  in  the  air  being  called  the  "aerial." 
The  transmitter  induces  electromagnetic  oscillations  in  the  aerial,  whence 
electromagnetic  waves  are  radiated  in  all  directions;  upon  reaching  the 
antenna  of  the  receiving  station  these  waves  again  produce  oscillations  in 
it,  thereby  causing  the  receiving  apparatus  connected  to  it,  to  respond. 

If  a  dot  of  the  Morse  Code  is  to  be  telegraphed,  the  electromagnetic 
waves  are  sent  out  for  only  a  very  short  instant,  while  if  a  dash  is  to  be 
telegraphed,  the  waves  are  sent  out  for  a  somewhat  longer  period. 

1.  THE  VARIOUS  KINDS  OF  ANTENNAE 

92.  Form  of  the  Aerials. — a.  The  simplest  form  of  antenna  consists  of 
a  vertical  wire  suspended  from  an  insulator:  "simple  antenna."     This  is 
nothing  more  nor  less  than  a  straight  lineal  oscillator. 

These  simple  antennae  are  no  longer  used  except  in  special  cases,  as, 
e.g.,  with  portable  stations,  on  airships  [Art.  96]  and  aeroplanes  and  where 
balloons  or  kites  are  used  to  carry  the  wire,  thereby  allowing  the  use  of 
great  lengths. 

The  successful  use  of  the  streams  of  water  as  simple  antennae  (R.  A. 
FESSENDEN142),  the  stream  being  maintained  by  a  pump,  is  mentioned 
mainly  as  a  curiosity.  Such  antennae,  while  very  disadvantageous 
because  of  their  high  ohmic  resistance*  may  nevertheless  be  useful  in 
special  cases  of  emergency  (e.g.,  in  a  fort  or  on  a  battleship  whose  normal 
antenna  has  been  destroyed  by  the  enemy's  fire). 

6.  The  use  of  a  large  number  of  nearly  vertical  wires  results  in  such 

*  A  transmitter  having  worked  480  km.  with  a  wire  antenna  40  m.  high,  worked 
over  a  distance  of  160  km.  with  a  stream  of  water  of  about  the  same  height  as  the 
wire  antenna. 

150 


THE  ANTENNA 


151 


forms  as  the  "harp"  or  "fan"  aerial  of  Fig.  183*  and  the  conical  or 
pyramidal  form  of  Fig.  184.  f  Fig.  185  shows  a  cross-section  of  a  double 
cone  or  double  pyramid  antenna. 


FIG.  1"83. 


FIG.  184. 


*  The  Italian  Battleship  "Carlo  Alberto,"  with  which  Marconi  made  long  distance 
tests  in  1902  (see  p.  117,  ZAMMARCHi1).  The  large  Eiffel  Tower  Station  has  a  harp- 
shaped  aerial,  stretched  from  the  top  of  the  tower.  Of  course  this  may  also  be  con- 
sidered merely  as  a  sector  of  an  umbrella  antenna. 

t  The  early  Poldu  Station  of  Marconi  for  long  distances.  This  antenna  was  long 
in  use  for  transmitting  telegrams  to  vessels  plying  between  Europe  and  America 
(see  p.  105,  ZAMMARCHi1). 


152 


WIRELESS  TELEGRAPHY 


c.  Antennae  having  very  great  capacity  at  their  upper  end1*3'*  are  now 
widely  used,  especially  the  so-called  "umbrella  antenna."  In  its  simplest 
form  this  consists  of  a  vertical  wire  or  bundle  of  wires,  from  the  upper 
end  of  which  wires  radiate  downward  in  all  directions,  sometimes  ex- 
tending quite  near  to  the  ground. 

The  form  used  by  the  TELEFUNKEN  Co.144  in  1910  for  the  construc- 
tion of  the  Nauen  Station  is  shown  diagrammatically  in  Fig.  186.  A  tower 


FIG.  185. 

100  m.  high,  terminating  below  in  a  carefully  insulated  ball,  serves 
partly  to  support  the  entire  antenna  and  partly  as  a  current  carrier  in 
conjunction  with  a  bundle  of  wires  with  which  it  is  connected. 

In  1911  this  tower  was  increased  to  a  height  of  200  m.  (Fig.  187) 
the  form  of  the  second  antenna  being  shown  in  Fig.  188.  In  April, 
1912,  during  a  severe  storm  this  tower  collapsed.  Shortly  after  the 
construction  of  an  entire  new  antenna  and  towers  was  undertaken. 


FIG.  186. 

A  similar  antenna  is  that  of  the  NATIONAL  ELECTRIC  SIGNALLING 
Co.'s  high-power  station  at  Brant  Rock147  (height  130  m.)  Its  um- 
brella consists  of  eight  cage-like  wire  structures  91  m.  long  and  1.2  m. 
in  diam.  Another  similar  antenna  is  that  of  the  high-power  station  at 
Eberswalde,  Germany  (C.  LORENZ). 

*  Probably  first  used  by  O.  LODGE  and  A.  MuiRHEAD145)  [Translator's  Note]. 
The  "flat  top"  antenna,  such  as  that  of  the  U.  S.  Naval  Station  at  Radio  (Arlington) 
also  belongs  to  this  class. 


THE  ANTENNA 


153 


However,  umbrella  antennae  are  also  often  used  for  portable  sta- 
tions. Many  ingenious  collapsible  masts148  of  light  weight  have  been 
devised  for  these,  so  as  to  be  easily  carried  on  pack-animals,  wagons,  etc., 
and  requiring  only  a  few  minutes  for  erection  and  taking  down. 


FIG.  187. 


.d.  Antennae  consisting  of  vertical  risers  which  are  then  prolonged 
horizontally  at  the  top,  usually  as  several  parallel  wires  (Fig.  189:  so- 
called  "F"  or  more  often,  "L"-antenna;  Fig.  190:  so-called  "^''-antenna), 


154 


WIRELESS  TELEGRAPHY 


18  Masts  .,— 


FIG.  189. 


FIG.  190. 


THE  ANTENNA 


155 


should  also  really  be  classified,  within  certain  limits,  among  the  antennae 
having  large  end  capacity.  They  are  especially  adapted  for  use  on 
board  ships,  as  the  horizontal  portion  can  be  conveniently  stretched 
between  the  masts.  Battleships  are  now  often  equipped  with  the  form 
shown  diagrammatically  in  Fig.  190$. 

A  number  of  other  forms,  which  may  be  considered  as  combina- 
tions of  two  of  the  forms  already  described,  have  also  been  proposed  or 
actually  used. 


FIG.  190a. 

93.  Comparison  of  the  Different  Forms  of  Aerials. — a.  It  is  evident 
that  the  effective  capacity  is  greater  in  all  of  the  various  complex  antennae 
described  than  in  a  simple  single  wire  antenna  of  the  same  height.  It 
is  greater  according  as: 

1.  The  distance  between   (spacing  of)   the  wires  is  greater  in  the 
vicinity  of  the  potential  anti-node  and  as 

2.  The  distance  from  the  wires  to  the  ground  is  less  at  this  part. 
Both  these  factors  give  the  umbrella  antenna  its  very  great  capacity 

in  comparison  to  other  forms.* 

6.  The  natural  frequency  of  the  complex  forms  described,  in  view 
of  their  greater  effective  capacity,  is  much  lower,  the  natural  wave- 
length therefore  much  greater  than  for  a  simple  antenna  of  the  same 
height. 

c.  As  to  the  current  distribution,  there  is  usually  a  current  anti-node 
at  the  base  of  the  antenna.  Thus  Fig.  44  shows  the  current  distribution 
for  a  simple  antenna  oscillating  at  its  natural  frequency;  a  current  node 
is  at  the  tip,  and  the  current  distribution  is  sinusoidal.  If  the  wave- 
length of  the  oscillation  is  materially  increased  by  inserting  a  coil  (self- 
induction)  near  the  base,  only  the  upper  and  nearly  straight  portion  of 
the  sine  curve  remains  [Art.  3 la].  For  conical  and  harp-  or  fan-shaped 
antennae,  the  current  distribution  curve  is  not  sinusoidal,  but  generally 
similar  to  the  heavy  broken  line  curve  in  Fig.  191. 

*  e.g.,  the  antenna  of  the  Nauen  Station,  Fig.  186,  had  an  effective  capacity  of 
about  0.018  MF. 


156 


WIRELESS  TELEGRAPHY 


A  characteristic  property  of  the  umbrella  type  of  antenna  is  the  fact 
that  the  current,  while  flowing  up  through  the  vertical  risers,  flows 
down  through  the  inclined  radial  wires.  The  current  distribution  in  the 
vertical  part  is  about  as  shown  by  the  heavy  broken  line  curve  on  the 


FIG.  191. 

right  side  of  Fig.  192,  while  in  the  inclined  wires  it  is  in  general  similar  to 
the  curve  on  the  left  side  of  Fig.  192;*  in  fact  these  forms  remain  practi- 
cally unchanged,  whether  the  oscillations  are  at  the  natural  frequency 
or  at  a  reduced  frequency  (increased  wave-length)  due  to  added  coils. 


FIG.  192. 

d.  Comparing  the  various  antennae  as  regards  distance  effect,  the  height 
being  the  same  for  all,  the  factors  which  enter  for  consideration  are 
[Art.  25]: 

*  The  latter  constructed  by  the  method  of  Art.  25d. 


THE  ANTENNA  157 

1.  The  frequency  (wave-length)  of  the  oscillation. 

2.  The  current  amplitude  at  the  current  anti-node.* 

3.  The  current  distribution,  hence  the  form  factor. 

Low  frequency  (great  wave-length)  is  unfavorable  for  good  radiation, 
but  favors  the  propagation  of  the  waves  through  space  [Art.  139/]. 

A  large  effective  capacity,  giving  a  large  current  amplitude  at  the 
current  anti-node*  and  a  current  distribution  favorable  to  good  distance 
effect  is  advantageous.  In  the  umbrella  antenna,  however,  the  portion 
which  is  useful  for  producing  distance  effect  is  relatively  small,  as  the 
currents  in  the  vertical  and  the  inclined  portions  tend  to  neutralize  each 
other's  effect,  leaving  only  the  shaded  area  shown  in  Fig.  192. 

2.  GROUNDING 

94.  Ground  and  Counterpoise.     Effect  upon  the  Current  Distribution. 

— If  an  aerial,  say  a  simple,  single  wire  antenna,  were  left  with  a  free  lower 
end,  it  would  have  a  current  node  at  the  lowest  point.  This  would  make 
it  quite  difficult,  to  say  the  least,  to  produce  strong  oscillations  in  the 
antenna  by  charging  it  or  by  coupling  it  to  a  primary  circuit,  f  Moreover, 
the  conditions  would  in  general  be  unfavorable.  Two  methods  for 
avoiding  this  are  in  use,  viz., 

1.  Direct  ground  connection  and 

2.  "Counterpoise,"  i.e.,  a  wire  network,  connected  to  the  lower  end  of 
the  antenna,  parallel  to,  but  insulated  from  the  ground.149 

a.  The  result  of  a  ground  connection  as  explained  in  Art.  33,  is  the 
formation  of  an  anti-node  of  current  at  the  base  of  the  antenna,  if  the 
ground  is  highly  conductive.  This  is  what  virtually  occurs  with  the 
waves  of  wireless  telegraphy  when  sea  water  or  very  moist  ground  exists 
at  the  base  of  the  antenna  for  a  considerable  distance  around  it.  This  is 
by  no  means  true,  however,  if  the  station  is  erected  upon  very  dry,  e.g., 
sandy  ground  or  upon  non-conducting  rocks,  {  ground  water  being  absent 
or  existing  only  at  a  great  depth.  In  such  cases  the  anti-node  of  current 
will  occur  higher  than  the  base,  the  height  increasing  as  the  conductivity 
of  the  ground  circuit  decreases. 

6.  The  effect  of  the  counterpoise  upon  the  current  distribution  is  not 
materially  different  from  that  of  a  direct  "ground,"  no  matter  what  the 
nature  of  the  soil.  We  must  distinguish  between  three  cases : 

*  At  a  given  potential  amplitude — the  same  coupling  with  the  same  primary 
circuit. 

t  The  spark  gap  [Art.  102a]  or  the  primary  circuit  [Art.  536]  would  have  to  be 
placed  at  a  considerable  height  above  the  ground. 

t  One  need  only  consider  the  fact  that  marble  and  slate  are  used  in  commercial 
light  and  power  circuits  as  good  insulating  materials  for  potentials  of  several  hundred 
volts. 


158  WIRELESS  TELEGRAPHY 

1.  The  ground  is  a  very  good  conductor. 

2.  The  uppermost  portion  of  the  ground  is  a  very  poor  conductor,  but 
underneath  this  at  a  slight  depth  there  is  conductive  ground  water. 

3.  The  ground  is  a  very  poor  conductor  and  either  there  is  no  ground 
water  at  all  or  only  at  very  great  depth. 

We  are  justified  in  assuming  that  a  condenser  of  considerable  capacity 
is  formed  in  the  first  case  by  the  counterpoise  and  the  surface  of  the  earth 
facing  it  and  in  the  second  case  by  the  counterpoise  and  the  surface  of  the 
ground  water  facing  it.  The  insertion  of  such  a  capacity,  however,  either 
does  not  change  the  current  distribution  at  all  or  it  may  raise  the  current 
anti-node  somewhat  [Art.  30]. 

The  third  case  is  identical  with  that  discussed  in  Art.  29 :  an  insulated 
conductor  of  great  capacity  is  connected  to  the  end  of  the  antenna. 

c.  The  practical  method  of  grounding  is  particularly  simple  in  the  case 
of  ships,  which,  in  nearly  all  instances  which  come  into  question,  are  con- 
structed of  metal,  so  that  connection  to  any  portion  of  the  ship's  body 
usually  suffices.  For  land  stations,  there  are  two  methods  mostly  in  use, 
viz., 

1.  A  metallic  plate  or  cylinder  (having  a  surf  ace  of ,  say,  a  few  square 
yards)  is  buried  in  the  ground  or  ground  water;  or 

2.  A  very  large  wire  network,  circular  or  square  shaped  is  laid  either  on 
top  of  or  in  the  ground.* 

The  counterpoise,  for  both  stationary  and  portable  stations,  is  usually 
provided  in  the  form  of  square  or  circular  wire  networks  or  radial  wires  in 
the  shape  of  a  star,  fastened  to  poles  a  few  feet  (say  2  or  3)  over  the  ground 
and  insulated  from  it.  For  portable  sets  a  rectangular  strip  of  wire  net- 
work, which  can  be  alternately  rolled  up  and  unrolled  and  fastened  to 
poles,  is  often  used  as  a  counterpoise. 

95.  Energy  Consumed  by  the  Earth  Currents.150— The  electric  field 
surrounding  an  antenna  exists  not  only  in  the  air,  but  also  partly  in  the 
ground.  Hence  there  must  be  currents  in  the  ground  which  dissipate 
energy.  It  is  impossible  to  generalize  as  to  the  extent  of  this  energy 
consumption,  which  depends  largely  upon  the  form  of  the  antenna,  the 
frequency  of  the  oscillations  and  the  nature  of  the  soil.  The  main  points 
which  come  into  consideration  are  about  as  follows : 

a.  Figs.  193-199f  illustrate  a  number  of  cases  diagrammatically,  it 
being  assumed  throughout  that  there  is  a  current  anti-node  at  the  base  of 

*  The  old  counterpoise  of  the  Nauen  Station  was  a  circular  wire  network  400  m. 
in  diam.,  placed  under  ground  at  a  depth  of  0.25  m. 

f  These  figures  are  not  based  upon  any  exact  calculations,  but  are  drawn  from  a 
general  consideration  of  each  set  of  conditions;  therefore  no  reliance  should  be  placed 
upon  their  precision.  H.  TRUEISO  has  investigated  the  course  of  the  ground  currents 
in  several  cases.  If  the  ground  has  extremely  low  conductivity,  the  electric  lines  of 
force  may  be  inclined  at  an  angle  to  the  surface  of  the  earth  for  a  short  distance  just 
above  the  ground  [Art.  139e]. 


THE  ANTENNA 


159 


FIG.  193. 


the  antenna.     Comparing  the  use  of  a  conducting  network  as  " ground" 
and  as  "  counterpoise,"  i.e.,  Figs.  195  and  197  with  Figs.  196  and  198,  we 
find  that  it  makes  no  difference 
qualitatively*  so  far  as  the  course 
of  the  current  lines  is  concerned, 
whether  the  network  is  buried  in 
the  earth  as  a  " ground"  or  used 
as  a  counterpoise. 

Both  cases,  however,  are  dis- 
tinctly different  from  the  case  of 
grounding  by  means  of  a  metal 
plate  (Figs.  193  and  194).  In 
the  latter  case  all  the  lines  of 
force  pass  from  the  antenna  into 
the  earth,  each  producing  cur- 
rents in  the  earth,  while,  where  a 
network  of  conductors  is  used,  a 
large  number  of  the  lines  of  force 
between  the  antenna  and  the  net- 
work pass  entirely  or  almost  en- 
tirely through  the  air,  thereby  dis- 
sipating no  energy,  f  Only  those 
lines  of  force  which  reach  the 
ground  outside  of  the  conducting 
network,  produce  currents  in  the 
earth.  Hence,  in  this  respect  such 
networks  are  far  superior  to  the 
use  of  relatively  small  metallic 
plates  as  grounds,  the  advantage 
increasing  as  the  area  of  the  net- 
work is  increased. 

From  this  point  of  view  the 
umbrella  antennae  (Fig.  199)  are 
particularly  advantageous.  If 
the  network  is  made  large  enough 
to  extend  considerably  beyond 
the  ends  of  the  inclined  radial 
wires  of  the  umbrella,  practically 
all  the  lines  of  force  will  pass 

*  However,  there  are  quantitative 
differences. 

t  That  is  if  we  neglect  the  heat  de- 
veloped  by  the   currents   in   the  coun- 
terpoise, or  in  the  case  of  a  grounded  network  (Fig.  195)  by  the  currents  between  the 
network  and  the  surface  of  the  earth. 


FIG.  194. 


FIG.  195. 


160 


WIRELESS  TELEGRAPHY 


from   the    antenna  to  the  network 


FIG.  196. 


FIG.  197. 


N 


"N      \ 


\ 

••  — 

\ 

X 

\ 

\ 

\ 

~~~x 

\        \ 

\ 

\ 

\    \ 

\ 

\ 

\ 
\ 
\ 

\  \ 

\ 

\ 

\       \ 

\ 

\      \ 

I      \ 

\         ] 

1 

\          \ 
\         \ 

FIG.  198. 


without  first  passing  through  the. 
earth. 

b.  In  Figs.  193,  195  and  197  it 
is  assumed  that  the  soil  is  homo- 
geneous and  has  very  low  con- 
ductivity,*  while  Figs.  194,    196 
and  198  are  based  on  the  assump- 
tion that  a  layer  of  ground  water 
of  relatively  high  conductivity  is 
present  at  a  short  distance  below 
the  surface,  underneath  an  upper 
stratum  of  very  low  conductivity. 
The  difference  lies  mainly  in  that 
the    lines    of    force    choose    the 
greater  part  of  their  path  through 
the    conducting  layer  of  ground 
water,  only  a  relatively  short  por- 
tion of  their   path   being   in   the 
upper    non-conducting    layer. 
When  grounding  by  means  of  a 
metallic  plate,  it  is  of  great  im- 
portance that  the  plate  is  placed 
at    a    sufficient   depth    to    really 
reach  the  ground  water  (Fig.  194.) 

c.  It  is  also  important  that  the 
lines  of  force  are  not  crowded  into 
a  very  narrow  space  at  any  point 
of  their  path,  as  this  always  in- 
volves a  relatively  great  dissipa- 
tion of  energy. 

For  instance  if  an  antenna  is 
grounded  through  a  single  vertical 
wire,  the  current  field,  as  seen 
from  above,  would  be  of  the  form 
shown  in  Fig.  200.  If  now,  as  is 
frequently  done,  the  ground  wire 
is  replaced  by  a  metallic  plate, 
the  current  field  assumes  a  far 
more  advantageous  form,  about 
as  shown  in  Fig.  201. 

If  the  wire  network  is  laid  on 
the  ground  so  as  to  be  in  (conduc- 


*  That  is,  ground  water  absent  or  present  only  at  great  depth. 


THE  ANTENNA 


161 


tive)  contact  with  it,  the  lines  of  force  follow  approximately  the  course 
shown  in  the  cross-section  drawn  in  Fig.  202  A  i.  If  portions  of  the  net- 
work do  not  make  intimate  contact  with  the  ground,  but  are  very  close 
to  it,  the  path  of  the  currents  is  not  materially  altered  (See  Fig.  202  A2). 
Fig.  203  shows  the  approximate  course  of  the  electric  lines  of  force  and 


FIG.  199. 

the  currents,  when  a  counterpoise  is  used  instead  of  a  direct  ground.  It 
certainly  is  the  more  advantageous  method ;  the  flow  into  the  ground  oc- 
curs just  as  if  the  network  were  replaced  by  a  sheet  of  metal  which  is 
conductively  connected  to  the  earth  at  all  points.  There  is  no  crowding 
of  the  current  lines  anywhere. 


\ 

\ 

/ 

\ 

f         ^ 

\      \ 

/       /' 

A  1 

1  (  ^-- 

:>  >  } 

\    ^^^. 

\     \ 

s    / 

\\ 

/ 

\ 

/ 

\ 

FIG.  200. 


FIG.  201. 


It  is  essential,  however,  that  the  conducting  network  which  forms  the 

counterpoise  is  really  insulated  from  the  ground.     Faulty  insulation  at 

any  point  may  come  under  either  of  two  classifications.     If  the  faulty 

insulation  still  offers  a  very  high  resistance  (e.g.,  a  damp  porcelain  insu- 

11 


162 


WIRELESS  TELEGRAPHY 


lator),  the  general  conditions  will  be  affected  but  very  slightly,  although 
of  course,  there  will  be  an  additional  loss  of  energy  in  the  high  resistance. 
But  if  the  resistance  is  very  low  where  the  fault  occurs  (e.g.,  a  spark  dis- 
charge to  ground)  a  very  considerable  portion  of  the  current  may  pass 
to  ground  at  this  point,  under  very  unfavorable  conditions,  similar  to 
those  shown  in  Fig.  200. 

d.  The  conductivity  of  the  soil  plays  an  important  part  in  determining 
the  course  and  density  of  the  ground  currents  as  well  as  the  energy  they 


Ai 

I     /       V    I    / 

v 


Az 
I    |   / 

* 


\    I     / 

V 


y  n 


FIG.  202. 

dissipate.  In  general,  for  a  given  form  of  antenna  and  a  given  frequency, 
there  exists  a  critical  value  of  the  conductivity,  at  which  the  energy  loss  is 
a  maximum.  For  any  other  conductivity,  be  it  greater  or  lower  than  the 
critical  value,  the  energy  dissipation  will  be  less. 

A  change  in  the  conductivity  of  the  ground  as,  for  example,  may  be 
caused  by  varying  weather  conditions  is  apt  at  times  to  result  in  a  change 
in  the  course  of  the  earth  currents,  in  the  damping  and  possibly  even  in 
the  frequency  of  the  oscillations.  The  earth,  therefore,  introduces  a 
variable  factor  into  the  entire  system,  no  matter  whether  we  use  a  direct 


\    /• 


i 


FIG.  203. 

ground  or  a  counterpoise.  Only  where  the  earth  possesses  very  high 
conductivity  (sea  water,  very  wet  soil)  does  the  effect  of  the  weather 
become  negligible. 

e.  If  we  let  Re  represent  the  equivalent  resistance,  of  such  value  that 
Relief  f  is  the  energy  consumed  per  second  by  the  earth  currents,  I  being 
the  current  amplitude  at  the  base  of  the  antenna,  then  it  follows  directly 
from  a  and  b,  that  this  ground  resistance,  Re,  must  depend  not  only 
upon  the  nature  of  the  soil  and  the  method  of  grounding,  but  also  upon  all 


THE  ANTENNA 


163 


those  factors  which  determine  the  electrical  field  in  the  earth,  and  hence 
particularly  upon  the  antenna  form  and  the  frequency  of  the  oscillations. 
As  regards  the  determination  of  Re  see  Art.  lOOd. 

Tests  with  an  umbrella  antenna  have  shown  that  Re  increases  to- 
gether with  the  frequency  of  the  oscillations,  but  decreases  as  the  height 
above  ground  of  the  counterpoise  (when  the  latter  is  used)  is  increased. 
In  all  cases  Re  was  lower  when  using  a  counterpoise  than  when  a  direct 
ground  of  the  form  shown  in  Fig.  193  was  used  (H.  TRUE150). 

96.  Ungrounded  Antennae  for  Airships.151 — a.  The  following  forms  of 
antennae  have  been  used  among  others,  for  airships,  where  grounding  of 
any  kind  is  entirely  out  of  the  question : 

The  antenna  is  a  wire  suspended 
from  the  car  (or  basket),  which  latter 
with  its  metal  parts  (motors,  etc.),  serves 
as  counterpoise,  insulated  from  the  bal- 
loon body  (the  bag).. 

2.  Similar    to    1,    except    that    the 
counterpoise  includes  the  metal  ribs  or 
frame   of  the  balloon    (as  in  the  Zep- 
pelin airships)  or  a  conducting    sheath 
of  the  balloon  in  addition  to  the  car. 

3.  The     antenna    consists    of     two 
wires*  of  unequal  lengths,  somewhat  on 
the    order    of    LECHER'S    arrangement 
(Fig.   204)    (H.   BEGGEROW):   e.g.,   one 
wire  (a i  &i)  is  made  equal  to  one-fourth 
of  the  wave-length  of  the   oscillations, 
the    other    (a2D)  =  %    wave-length. 

The  oscillations  are  produced  at  A  in  the  car;  nodes  of  potential  will 
then  occur  at  A  and  C  (see  Arts.  72c2  and  24a).  So  far  as  radiation 
is  concerned,  only  the  part  BD,  which  forms  a  simple  lineal  antenna, 
is  effective,  as  the  portions  ai&i  and  a262  neutralize  each  other. 

4.  For  directive  antennae,  adaptations  of  Fig.  416  have  been  suggested; 
the  horizontal  part  is  stretched  out  underneath  the  dirigible,  parallel  to  its 
axis,  while  the  two  vertical  antennae  are  suspended  downward. 

6.  With  balloons  there  is  ever  present  the  danger  of  sparks  between 
any  parts  of  the  balloon  having  considerable  potential  differences  caused 
by  the  oscillations  in  the  antenna  when  transmitting,  f 

Such  differences  of  potential  may  be  the  result  of  various  causes,  thus : 

1.  If  any  part  of  the  airship  is  conductively  connected  to  the  antenna, 
the  oscillations  of  the  latter  are  spread  out  over  the  entire  metal  structure 
of  the  airship.  This  results  in  differences  of  potential  between  individual 

*  Which  are  kept  at  the  same  distance  apart  throughout  by  insulating  spacers. 

f  Normally,  of  course,  the  oscillations  during  reception  are  entirely  harmless. 


164  WIRELESS  TELEGRAPHY 

parts  of  the  airship.  To  avoid  these,  it  is  advisable  to  join  all  neighboring 
metallic  parts  of  the  airship  by  the  shortest  possible  connecting  leads  or 
bonds. 

2.  The  electric  field  of  the  oscillations  may  produce  differences  of 
potential  (" influence"  action)  between  individual  parts  of  the  airship. 
This  danger  is  greatly  lessened  by  keeping  the  anti-node  of  current  far 
from  the  airship. 

3.  The  magnetic  field  of  the  oscillations  may  induce  currents  in  the 
metal  parts  of  the  airship.     In  this  connection  a  node  of  potential  or 
anti-node  of  current  in  the  antenna  is  particularly  dangerous152. 

In  short  there  are  so  many  possible  tendencies  for  the  production  of  a 
spark,  that  it  is  probably  impossible  to  state  in  advance  that  any  particu- 
lar arrangement  is  spark  proof.  On  the  other  hand,  none  of  the  arrange- 
ments described  in  A  need  be  feared  as  placing  an  airship  in  any  con- 
siderable danger. 

In  general,  it  may  be  stated  that  short  wave-lengths  are  usually  more 
dangerous  than  long  ones,  and  that  the  danger  diminishes  with  decreasing 
current  and  potential  amplitudes.  Accordingly  arrangements  involving 
a  comparatively  small  amount  of  oscillating  energy  but  having  a  high 
discharge  frequency  are  advantageous  when  compared  to  those  of  equal 
total  energy  but  using  larger  amplitudes  (energy)  for  each  oscillation  at 
lower  frequencies.153 

c.  There  is  of  course  also  the  danger  of  gas,  which  has  escaped  from  the 
balloon,  becoming  ignited  by  the  sparks  in  the  gap  of  the  primary  circuit. 
It  is  obvious  that  only  completely  enclosed  gaps  [e.g.,  see  Art.  Ill]  should 
be  used. 

3.  THE  OSCILLATIONS  OF  ANTENNA 

97.  Frequency,  Capacity  and  Self -induction.154 — a.  To  measure  the 
natural  frequency  of  an  antenna,  cause  a  loop  or  coil  of  wire  inserted 
in  the  antenna  to  act  inductively  upon  a  measuring  circuit,  then  pro- 
ceed according  to  any  of  the  methods  already  described  [Art.  71].  A 
small  spark  gap  in  the  antenna  or  preferably  a  quenched  gap  circuit  or 
impulse  excitation  [see  Art.  78]  serves  to  produce  the  oscillations.  Or  a 
primary  circuit  having  a  known  and  variable  frequency,  is  loosely 
coupled  to  the  antenna  and  its  frequency  adjusted  until  a  measuring 
instrument  in  the  antenna  gives  the  maximum  deflection. 

6.  Frequency  measurements  may  also  serve  for  determining  the 
effective  capacity,  C,  and  the  effective  coefficient  of  self-induction,  L,  of  the 
antenna  [Art.  27a],  for  example,  as  follows: 

1.  A  coil  of  known  self-induction,  L0,  is  inserted  at  the  current  anti- 
node.  This  will  change  the  frequency  N  to  Nf,  the  wave-length  X  to  X'. 
Then  N,2  X2 

L  =  LO     Z  _     ,2  =  Lo/8  _2    approx.  (1) 


THE  ANTENNA  165 


Applying  this  value  of  L  to  the  equation  [Art.  27a] 

N  "= 


or 

X  =  2irVLVLC  (2) 

the  value  of  C  is  obtained.  . 

2.  A  condenser  of  known  capacity,  COJ  is  inserted  at  the  current  anti- 
node.  Then  if  the  new  values  of  the  frequency  and  wave-length  are  N" 
and  X"  respectively,  we  have, 

JV"2  —  N2  X2  —  X"2 

C  =  Co  --  ^2  --  =  Co—   /T^  —  approx.  (3) 


Again  applying  the  value  of  C  to  equation  (2)  we  obtain  L. 

It  is  advisable  to  apply  both  methods  1  and  2,  and  use  the  average 
of  the  two  values  obtained  for  L  and  C.  The  greater  the  difference 
between  N  and  N'  or  N  and  N"  the  less  will  be  the  danger  of  inaccurate  re- 
sults, while  if  these  differences  are  small,  N9  Nf  and  N"  must  be  deter- 
mined with  great  precision.* 

c.  Another  method  (C.  FISHER),  which  however  is  neither  so  con- 
venient nor  so  accurate,155  consists  in  the  insertion  of  a  resistance  R  at 
the  anti-node  of  current  in  the  antenna  and  measuring  the  decrement 
before  (di)  and  after  (dz)  inserting  R.  Then  we  have  for  the  difference 
of  the  two  decrements 


d  =  d2  -  di  =  irfl-Jjr     [Art-  27al 

Combining  this  with  equation  (2)  which  gives  the  product  C  X  L,  we 
obtain  both  C  and  L. 

98.  Regarding  the  Effect  of  Coils  and  Condensers  in  Antennae. — a. 

The  insertion  of  coils  (inductance)  lowers  the  frequency,  hence  increases 
the  wave-length,  f  decreases  the  form  factor  and,  with  a  given  potential 

*  The  following  are  typical  antenna  capacities  mentioned  in  the  literature  of 
wireless  telegraphy. 

Torpedo  boat  antenna C  —  approx.      1  X  10~3  MF. 

Cruiser,  battleship   antenna C  =  approx.      2  X  10~3  MF. 

Brant  Rock  high-power  station C  =  approx.      7  X  10~3  MF. 

Nauen  high-power  station C  =  approx.     18  X  10~3  MF. 

Eiffel  Tower  high-power  station C  =  approx.  7.  3X  10~3  MF. 

The  self-induction  used  in  antennae  is  usually  much  greater  than  that  of  the  aerial 
proper  due  to  inductive  coils  in  the  antenna  circuit.  The  self-induction  of  the  Brant 
Rock  aerial  is  given  as  55,000  C.G.S.  units,  that  of  the  Eiffel  Tower  as  196,000  C.G.S. 
units. 

fThis  is  often  expressed  as  "lengthening  the  antenna"  (aerial)  by  means  of  a 
coil  and  "shortening"  it  by  a  condenser. 


166 


WIRELESS  TELEGRAPHY 


amplitude,  decreases  the  current  amplitude  [see  Fig.  47,  Art.  31].  All 
these  effects  tend  to  reduce  the  radiation  and  also  the  radiation  decrement. 
The  insertion  of  a  condenser  at  the  base  of  an  antenna  has  the  oppo- 
site effect,  in  so  far  as  it  increases  the  frequency,  hence  decreases  or  short- 
ens the  wave-length*  and  at  the  same  time  the  anti-node  of  current  is 
raised  upward  from  the  base  of  the  antenna  [Art.  30].  The  form  factor 
is  thereby  made  more  favorable  for  distance  effect.  As  to  the  change  in 
the  current  amplitude  with  respect  to  the  poten- 
tial  amplitude  and  as  to  the  resultant  change  in 
the  distance  effect  and  radiation  decrement,  it 
is  hardly  possible  to  draw  any  conclusions  to 
cover  all  the  various  forms  of  antennae. 

By  inserting  both  a  coil  and  condenser  in 
series,  these  can  be  so  chosen  for  any  given  aerial 
as  to  avoid  any  change  in  the  wave-length, 
only  greatly  reducing  the  radiation  decrement 
("Antenna  with  reduced  radiation  damping"  [see 
Art.  326]. 

b.  Instead  of  using  just  coils,  the  wave- 
length of  an  antenna  can  be  greatly  increased 
by  means  of  the  arrangement  shown  in  Fig. 
205. f  A  coil,  L,  whose  self-induction  is  very 
great  as  compared  to  that  of  the  aerial  and  the 
connection  to  ground  is  inserted  in  series  with 
the  antenna  and  the  condenser,  C,  is  joined  in 
parallel  to  it.  We  are  justified  in  considering 
this  arrangement,  as  used  in  practice,  as  form- 
ing a  condenser  circuit  whose  self-induction  is 
practically  that  of  the  coil  L  and  whose  capac- 
ity  consists  of  the  condenser  C  in  parallel  with 
the  capacity  formed  by  the  aerial  and  ground. 
A  little  consideration  will  make  it  evident  that 
such  an  arrangement  has  a  materially  lower 
radiation  decrement  than  the  antenna  alone. 

c.  These  arrangements  have  found  practical  application  as  follows: 

1.  In  order  to  make  the  advantage  of  long  waves  for  propagation 
available,  it  is  customary  to  use  coils  of  considerable  self-induction  in 
antennae,  either  alone  or  in  conjunction  with  condensers  (" Lengthen- 
ing Coils")  [see,  e.g.,  the  coil  marked  28  in  Fig.  236]. 

2.  Coils  of  adjustable  self-induction  at  times  together  with  condensers, 
or  condensers  of  adjustable  capacity  alone  are  universally  used  for  tuning 

*  This  is  often  expressed  as  " lengthening  the  antenna"  (aerial)  by  means  of  a 
coil  and  "shortening"  it  by  a  condenser. 

t  This  is  sometimes  called  the  "fly-wheel"  method. 


FIG.  205. 


THE  ANTENNA  167 

antennae  to  a  desired  wave-length  ("tuning  coils,"  "tuning  condensers," 
"aerial  variometers"). 

3.  To  obtain  different  wave-lengths  with  the  same  antenna,  a  conden- 
ser, at  times  with  a  coil  in  series,  is  so  connected  that  it  may  be  cut  into 
(short  waves)  or  out  of  (long  waves)  the  antenna  by  means  of  a  switch. 
Or  a  switch  is  arranged  by  means  of  which  the  condenser  is  connected  in 
series  with  the  aerial  for  short  waves  (Fig.  206)  and  in  paral- 
lel to  the  coil  (Fig.  205)  for  long  waves.  A 

99.  The  Damping  of  Antennae  and  Its  Causes. — a.  Only 
that  portion  of  the  energy  which,  during  the  oscillations  of 
an  antenna,  is  sent  out  in  the  form  of  electromagnetic  waves, 
may  be  considered  as  useful  energy.  If  then  we  wish  to 
speak  of  the  "efficiency"  of  an  antenna,  meaning  thereby 
the  relation  of  the  useful  energy  to  the  total  energy  supplied, 
at  the  fundamental  oscillation,  this  would  be 


i.e.,  the  ratio  of  the  radiation  decrement  to  the  total  decre- 
ment.* 

b.  All  other  losses  of  energy  which  occur  during  the 
oscillation,  are  more  or  less  necessary  evils.  These  include : 

1.  Joulean  heat  in  the  antenna. 

2.  Joulean  heat  of  the  earth  currents. 

3.  Joulean  heat  of  the  induced  currents. 

4.  Losses  due  to  brush  (leakage)  discharge. 

5.  Circuit  losses. 

The  development  of  heat  (Joulean)  in  the  wires  of  the 
aerial,  in  the  tuning  and  lengthening  coils,  in  the  ground  cir- 
cuit, in  the  counterpoise  and  in  the  various  leads,  has  a 
considerable  effect  upon  the  decrement  of  such  antennae 
whose  radiation  decrement  has  been  much  reduced. 

Hence  for  well-designed  antennae  it  is  customary  to  use  braids  of  very 
fine,  individually  insulated  wires,  or  bands  or  strips  consisting  of  several 
such  braids  in  parallel  and  interwoven,  in  order  to  reduce  the  ohmic  resist- 
ance to  a  minimum,  f 

*  COUNT  v.  ARCO157  estimates  the  efficiency  of  a  properly  constructed  ship  antenna 
at  50  per  cent.,  if  the  wave-length  is  increased  by  the  factor  1.3  by  means  of  inserted 
coils. 

t  COUNT  v.  ARCO160  gives  the  following  data: 

2  kw.  station:  effective  current  at  base  of  antenna,  13  amp.;  antenna  resistance, 
6  ohms;  480  single  wires  in  parallel. 

8  kw.  ship  station:  effective  current  at  base  of  antenna,  35-40  amp.;  antenna 
resistance  3  ohms;  3000  wires  in  parallel.  To  provide  the  necessary  tensile  strength 
copper-sheathed  steel  wires  [Art.  36c]  and  also  bronze  wires  are  often  used. 


168  WIRELESS  TELEGRAPHY 

The  portion  of  the  total  decrement  due  to  the  earth  currents  may  at 
times  be  as  large  as  the  radiation  decrement.  Even  in  spite  of  the  greatest 
precautions  in  grounding,  in  the  attempt  to  keep  this  portion  of  the 
decrement  at  a  minimum  the  results  will  depend  ultimately  upon  the 
nature  of  the  soil.  Such  results  as  can  be  obtained  at  sea  are  probably 
never  attained  over  poorly  conducting  ground.153 

Induced  currents  come  mainly  into  question  in  guys,  stays,  iron  masts 
and  similar  metal  parts  on  board  ships,  and  in  the  towers  supporting  the 
antennae  and  their  guys  in  land  stations.  Experience  has  shown  that 
these  currents,  which  always  mean  a  waste  of  energy,  may  harm  the 
radiation  considerably  and  be  generally  detrimental.  A  method  of  coun- 
teracting the  bad  effect  of  these  currents  is  to  insert  insulating  links  in  the 
conductors  affected,  or,  in  any  case,  insulating  them  from  ground.  This 
was  very  well  provided  for  in  the  old  Nauen  antenna  [Art.  92c];  the  only 
conducting  parts  in  which  currents  could  be  induced  were  the  three  guys 
holding  the  tower  and  these  were  well  insulated  from  the  tower  at  their 
upper  ends  and  from  the  ground  below.159 

It  is  well  known  that  the  brush  or  leakage  discharge,  which  at  night  is 
visible  over  a  large  part  of  the  antenna,  has  a  very  bad  effect  upon  the 

*  ?>  a 


FIG.  207. 

decrement;  it  is  therefore  important  to  avoid  sharp  points  and  edges  in 
the  aerial.  As  increased  surface  (larger  radius  of  curvature)  for  the 
conductors  tends  to  reduce  the  brush  discharge,  it  has  been  proposed  to 
surround  the  antenna  wires  by  metal  piping  or  tubing  joined  conductively 
to  the  wires  (Fig.  207),  or  else  to  use  metal  bands  or  strips,  preferably 
having  rounded  edges,  wound  around  rope,  as  the  aerial  conductors. 
The  use  of  well-insulated  high-tension  cable  instead  of  bare  wire  is 
perhaps  even  more  effective.  Specially  designed  insulators1™  to  prevent 
brush  discharge  are  frequently  used  at  the  ends  of  the  wires. 

Circuit  losses*  may  of  course  occur  in  any  oscillator  such  as,  e.g.,  a 
condenser  circuit.  They  have  not  been  previously  discussed  for  the  rea- 
son that  they  are  easily  prevented  in  all  other  forms  of  oscillators  and 
hence  are  of  no  importance  when  ordinary  precautions  are  taken.  With 
antennae  as  used  in  radio-telegraphy,  however,  the  prevention  of  circuit 
losses,  in  view  of  the  high  potentials  involved  and  the  severe  weather 
effects156  is  a  much  more  difficult  matter. 

100.  Determination  of  the  Decrement. — a.  Any  of  the  methods 
already  given  may  be  applied  to  find  the  total  decrement  of  the 'natural 
oscillations;  a  quenched  gap  circuit  offers  a  suitable  means  for  excitation. 

*  This  is  intended  to  include  losses  due  to  spark  discharges  (to  ground,  etc.). 


THE  ANTENNA 


169 


The  value  of  the  total  decrement  for  various  forms  of  antennae  under 
normal  conditions  (good  grounding,  thorough  insulation),  there  being  no 
coils  of  great  self-induction  inserted,  runs  about  as  follows: 

Simple  antenna  (single  straight  wire,  airship  antenna) .  0 . 25-0 . 3 

Harp-  or  fan-shaped  antenna 0.2 

Conical  or  double-cone  antenna 0 . 16-0 . 18 

Umbrella  or  ship  (T)  antenna 0 . 12-0 . 16 

As  a  matter  of  fact,  inductive  coils  are  always  inserted.  If  their 
coefficient  of  self-induction  is  not  sufficiently  large  to  materially  affect 
the  frequency  of  the  oscillations,  the  decrement,  for  umbrella  and  ^-aerials 
will  be  about  0.1.  But  if  the  wave-length  is  increased  to  three  or  four 
times  its  original  value  by  means  of  induc- 
tance inserted  in  these  forms  of  antennae, 
the  total  decrement  can  thereby  be  reduced 
to  0.05-0.03. 

b.  The  effective  resistance,  R,  can  be  cal- 
culated, if  the  total  decrement,  d,  is  known, 
from  the  equation 

d  =  irR  >£       [Art.  27a] 


if  C  and  L  are  also  known. 

R  may  also  be  found  by  causing  an  un- 
damped primary  circuit  to  act  inductively 
upon  the  antenna  and  then  proceeding  as 
per  Art.  766.161 

The  following  (" artificial  aerial")  method 
has  also  been  widely  used: 

A  primary  circuit  (quenched  gap  circuit  or  undamped  oscillations) 
can  be  loosely  coupled  by  means  of  the  switches  U\  and  U2  (Fig.  208), 
either  with  the  antenna  (E  —  S2  —  aerial)  or  (dotted  position  of  switches) 
with  a  condenser  circuit  S2S'2CR,  having  the  same  capacity  and  self- 
induction  as  the  antenna,  but,  in  addition,  a  variable  resistance,  R.  The 
latter  is  adjusted  until  the  ammeter,  A,  gives  the  same  reading  (current 
effect)  with  either  the  aerial  or  the  condenser  circuit.  Then  the  resist- 
ance of  the  condenser  circuit  =  the  desired  effective  resistance  of  the 
antenna. 

In  order  that  the  resistance  of  the  condenser  circuit  may  be  easily 
determined,  it. is  advisable  to  so  construct  it  that  its  resistance  shall  be 
very  small  as  compared  to  that  of  the  variable  resistance  R,  the  latter 
being  made  of  such  wires  and  so  designed  that  its  effective  resistance  =  its 
D.C.  resistance  [Art.  366],  so  that  it  may  be  measured  with  direct  current. 

c.  It  is  particularly  interesting  to  separate  the  radiation  resistance 
from  the  other  parts  that  make  up  the  total  resistance. 


FIG.  208. 


170  WIRELESS  TELEGRAPHY 

If  the  form  factor  of  an  antenna  has  been  found  by  current  measure- 
ments and  the  antenna  stands  on  soil  of  good  conductivity,  the  radiation 
resistance  can  usually  be  calculated  with  sufficient  accuracy. 

In  this  case  the  field  of  the  grounded  antenna  (height,  h)  over  the 
surface  of  the  earth  is  identical  with  the  field  which  would  result  from  the 
antenna  and  its  "image,  "  i.e.,  an  oscillator  whose  total  length  I  =  2h,  there 
being  no  ground  present.  The  only  difference  is  that  the  energy  radiation 
of  the  grounded  antenna  is  only  one-half  the  radiation  of  this  oscillator,  as 
in  the  former  the  lower  half  is  missing  [Art.  33]. 

Hence  if,  according  to  Art.  286,  the  radiation  resistance,  R?}  of  this 
oscillator  of  length  I  is  given  by 


then  for  the  grounded  antenna  this  must  be 


=  1607r2 


/ah\ 

(T) 


in  which  a  has  the  values  given  in  Art.  25c.  With  sinusoidal  current  dis- 
tribution (simple  antenna)  R%  =  36.6  ohms  [Art.  266]. 

The  following  is  an  experimental  method  (A.  ERSKINE-MURRAY,  M. 
REicH162)  for  approximately  determining  the  radiation  resistance  of  a 
transmitting  antenna.  At  a  distance,  r,  of  at  least  several  wave-lengths 
from  the  transmitting  aerial,  a  tuned  receiving  aerial  is  erected  and  the 
current  effects  /i2e//  and  /22C//  determined  at  the  bases  of  the  sending  and 
receiving  antennae  respectively.  The  height  of  the  transmitting  aerial  is 
then  altered  a  little  (say,  by  simply  raising  or  lowering  the  aerial  wires 
slightly  by  means  of  ropes)  and  the  measurements  repeated,  giving  the 
new  values,  I'i2e//  and  / Ve//-  The  discharge  frequency  and  wave-length 
must  be  retained  constant.  This  method  assumes  that  the  electric  field 
at  the  distance  of  the  receiving  antenna,  and  also  the  ground  resistance 
near  the  transmitter  are  not  appreciably  changed  by  the  change  in  the 
height  of  the  aerial  wires — an  assumption  which  of  course  is  not  always 
correct. 

Under  these  conditions  we  then  have  the  following  relations:! 

Conceive  a  sphere  of  radius,  r,  surrounding  the  transmitting  antenna. 
Then  the  energy  which  passes  through  a  square  centimeter  of  the  surface 
of  the  sphere  per  second  ex  E2eff,  E  being  the  electric  field  strength  at 
the  point  in  question  [Art.  26] ;  it  also  oc  E<?eff,  E2  being  the  electric  field 

*  =  1607T2 1  — }    ohms,  if  h'  =  ah  is  the  effective  height  of  the  antenna. 

f  What  follows  is  based  on  the  assumption  of  good  conductivity  of  the  soil.  The 
results,  however,  are  not  dependent  upon  this  assumption. 


THE  ANTENNA 


171 


strength  at  the  receiving  antenna,  or  it  °c  S2e//,  S  being  the  potential 
difference163  acting  along  the  length  of  the  receiving  antenna. 

Hence,  the  total  energy  which  passes  through  the  entire  surface  of  the 
sphere  each  second  also  oc  S2e//.  On  the  other  hand  it  is  =  jRs  .  /i2e// 
[Art.  26].  Hence  we  obtain 


Jl   eff 

The  relation  of  I2  to  E  depends  upon  whether  the  oscillations  of  the  trans- 
mitting antenna  are  damped  or  undamped.     In  the  latter  case 

72  =  A  [Art.  67  &];  I^eff  =  -~f 
hence,   we  may  write 


*ff 


But  if  the  antenna  oscillations  are  damped,  then 

[Art.  44a] 
1 


c?id2(d] 


[Art.  70,  Equation  (1)] 


P 


and 


+  cfe) 


e// 


ISe 


If  now  we  let  R  and  J?r  represent  the  effective  resistance  of  the  trans- 
mitting antenna  during  the  two  measurements  respectively,  and  R0)  that 
part — constant  by  our  assumption — which  is  not  due  to  the  radiation 
decrement,  then  for  undamped  oscillations  we  have 


R      =   RQ  -f-  1^2   =  ^0  ~h  ^  • 


and  for  damped  oscillations 

r>  7") 

It      —    /to  " 


^// 


1   eff 


(1) 


d(di  +  d2) . 


d(d( 


eff 


/I2 


ejf 


(2) 


*  a,  6,  d  and  p  are  factors  of  proportionality.     This  d  should  not  be  confused  with 
the  decrements. 


172  WIRELESS  TELEGRAPHY 

Subtracting  one  equation  from  the  other,  we  obtain  b  or  d  and  thereby 
the  radiation  resistance,  7£s,  having  previously  determined  the  total  effect- 
ive resistance,  R  and  Rr  and  also,  when  damped  oscillations  are  used,  the 
sum  of  the  decrements  [(di  +  ck)  and  (d\  +  cZ2*)]. 

A  test  of  whether  the  assumptions  upon  which  the  preceding  equations 
were  based  hold  approximately  true  in  a  given  case  can  be  obtained  by 
repeating  the  measurements  at  one  or  two  different  antenna  heights;  the 
additional  equations  so  obtained  should  give  the  same  resulting  values 
for  b  and  d. 

d.  Having  determined  the  radiation  resistance  R?  and  the  effective 
resistance  Rj  of  the  aerial  wires,  as  well  as  the  total  antenna  resistance 
R,  then  from 

R  —  R?  +  Rj  +  Rej 

the  value  of  Re  follows.  This,  for  antennae  on  firm  ground,  seems  to 
amount  to  at  least  several  ohms,150  but  depends  entirely  upon  the  form  of 
the  antenna,  the  frequency  of  the  oscillations,  the  nature  of  the  soil  and 
the  method  of  grounding. 

*  If  di  and  d'^d^  equation  (1)  may  be  applied  to  damped  oscillations  also. 


CHAPTER  VII 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 

101.  The  Different  Types  of  Transmitter. — There  are  two  methods, 
customarily  applied  for  producing  the  oscillations  in  the  antenna,  viz., 

a.  A  spark  gap  is  inserted  in  the  antenna  and  the  latter  is  charged  by 
means  of  an  induction  coil  or  its  equivalent.     The  antenna  discharges 
across  the  gap,  during  which  discharge  the  antenna  oscillates  in  its 
natural  period.     This  is  the  "simple"  or  "Marconi  transmitter.' * 

b.  The  antenna  is  coupled  to  a  condenser  cir- 
cuit.    This  gives  rise  to  two  possible  cases,  viz., . 

1.  Two  coupling  oscillations  are  produced  in 
both  the  condenser  circuit  and  the  antenna — the 
"Braun  transmitter,"  or 

2.  The  oscillations  of  the  condenser  circuit  are 
quenched  after  a  few  cycles  and  the  antenna  con- 
tinues to  oscillate  with  its   own    damping — the 
"quenched  spark  gap"  or  "Wien  transmitter." 

1.  THE  SIMPLE  (MARCONI)*  TRANSMITTER 

102.  General. — a.  The  antenna  has  a  spark 
gap,  F  (Fig.  209)  at  the  bottom. 

It  is  advantageous  to  have  an  anti-node  of  FlG   2Q9. 

current  at  the  foot  of  the  antenna,  for,  with  a  given 

voltage,  this  will  make  the  current  amplitude  of  the  fundamental  oscil- 
lation a  maximum  and  the  spark  damping  a  minimum,  with  the  spark 
gap  lying  in  an  anti-node  of  current.  This  condition  is  no  doubt 
always  obtained  in  practice  by  grounding. 

b.  The  combined  or  multiple  forms  of  aerials  [see  Art.  92]  increase  the 
effectiveness  of  the  MARCONI  transmitter.  For  the  same  height,  their 
effective  capacity  is  much  greater  and  if  their  form  is  properly  chosen,  the 
current  distribution  along  the  antenna  is  much  better  than  with  the 
simple  aerial.  Both  these  differences  are  factors  favoring  increased 
distance  effect  at  a  given  voltage  [Art.  93d. 

*  MARCONI  now  also  uses  the  coupled  BRAUN  transmitter  exclusively  or  at  least, 
mainly,  for  damped  oscillations.  However,  it  was  with  the  simple  form  of  transmitter 
that  he  attained  his  first  successful  results  and  demonstrated  the  possibility  of  wireless 
telegraphy  by  means  of  electromagnetic  waves  over  great  distances. 

173 


174  WIRELESS  TELEGRAPHY 

103.  The  Damping. — a.  Any  of  the  spark  methods  of  excitation  inher- 
ently involve  a  consumption  of  energy  in  the  spark  in  addition  to  the 
energy  losses  occurring  in  antennae  without  spark  gaps.  Accordingly, 
the  efficiency  is  not  as  high  as  for  an  antenna  without  a  gap.  If  we 
define  the  efficiency,  as  in  Art.  99cc,  as  the  ratio  of  the  energy  radiated  by 
the  fundamental  oscillation  in  useful  form  to  the  total  energy  consumed 
by  it  in  the  same  time,  we  have 

d? 


where  d  is  the  decrement  of  the  antenna  without  the  gap  and  d0  is  the 
spark-gap  decrement. 

If,  however,  we  conceive  the  efficiency  as  the  ratio  of  the  useful  energy, 
radiated  at  the  fundamental  oscillation  to  the  total  energy  supplied  to  the 
antenna  by  charging,  the  result  is  even  less  favorable.  In  the  MARCONI 
transmitter  there  necessarily  exist  at  the  start  not  only  the  fundamental, 
but  also  a  series  of  partial  oscillations.  These  are  of  no  use  so  far  as  the 
distance  effect  is  concerned,  as  the  receivers  are  always  tuned  to  the 
fundamental  oscillation.  Hence  the  energy  consumed  in  one  form  or 
another  by  the  upper  partial  oscillations  represents  a  further  loss  which 
causes  an  additional  decrease  in  the  efficiency. 

6.  From  observations  made  to  date,  it  appears  that  with  a  given 
antenna,  the  effect  of  the  oscillations  and  also  the  distance  effect  do  not 
increase  as  the  spark  length  is  increased  beyond  a  certain  point,  in  fact, 
they  decrease  beyond  this  point.*  Apparently  this  turning  point  occurs 
earlier,  according  as 

1.  The  effective   capacity  of  the  antenna  is  smaller  (hence  in   this 
respect  a  multiple. antenna  is  preferable  to  a  simple  antenna); 

2.  The  radius  of  curvature  of  the  gap  electrodes  is  smaller  (hence  large 
spheres  or  plates  are  better  than  small  spheres). 

c.  In  tuned  telegraph  operation,  the  MARCONI  transmitter  is  at  a  dis- 
advantage on  account  of  the  great  damping  of  the  oscillations,  although 
this  is  in  part  only  a  factor  of  strong  distance  effect.  MARCONI  trans- 
mitters can  be  constructed  with  decreased  radiation  damping  [Art.  98] 
and  a  total  decrement  of  about  0.1.  But  the  weak  distance  effect  of 
such  a  transmitter  requires  a  very  high  potential  if  long  distances  are 
to  be  attained  in  telegraphing.  This  leads  to  such  insulation  difficulties, 
that  the  reliability  of  such  transmitters  becomes  uncertain  for  regular 
operation,  even  though  they  may  have  shown  good  results  under  first 
tests. 

*  It  is  questionable  whether  this  is  due  solely  to  the  influence  of  the  changed  gap 
length.  Presumably  brush  discharge,  and  circuit  losses  played  an  important  part 
in  these  experiments. 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


175 


2.  THE  BRAUN*  TRANSMITTER 

104.  Nature  of  the   Coupling. — The   coupled   (BRAUN)   transmitter 
consists  of  a  condenser  circuit,  the  u  excitation 
circuit"    as    primary    and    the    antenna    as 
secondary  circuit.     The  primary  and  second- 
ary circuits  are  tuned  so  as  to  be  in  resonance. 

a.  The  coupling  may  be  purely  magnetic, 
inductive,  or  it  may  be  direct,  conductive  [Art. 
526].  The  former  is  shown  diagrammatically 
in  Fig.  210,  the  latter  in  Figs.  211  and  212. 
With  direct  coupling  the  secondary  circuit  is 
comprised  of  the  aerial  proper  (plus  BA  in 
Fig.  212),  a  portion  (BE  in  Fig.  211  and  AE 
in  Fig.  212)  of  the  condenser  circuit  and  the 
line  to  ground,  or,  if  a  counterpoise  is  used, 


FIG.  210. 


1.0 


FIG.  211. 


this  and  its  leads. 

In  addition  to  these,  mixed 
or  combined  forms  of  these 
arrangements  have  been  used 
or  are  still  partly  in  use  (e.g., 
Fig.  213). 

_^  6.  The  direct  and  the  in- 

^— -^  p  ductive  connections  do  not 
give  materially  different  re- 
sults. The  direct  coupling 
has  the  advantage  of  simplic- 
ity; above  all  it  avoids  the 
necessity  of  insulating  the 
primary  and  secondary  turns 
from  each  other,  which  to  say 


the  least  involves  considerable  inconvenience 
for  the  inductive  arrangement.  Direct 
coupling  is  now  in  very  wide  use;  the  in- 
ductive or  mixed  form  is  possible  only  for 
very  close  coupling. 

105.  Coupled  Transmitter  for  Antennae 
having  High  Damping.  Very  Loose  Coup- 
ling.— Under  highly  damped  antenna  are 
to  be  understood  such  whose  decrement 


FIG.  213. 


*  F.  BRAUN  was  probably  the  first  to  introduce  the  coupled  transmitter  into  the 
practise  of  radio-telegraphy.  His  patent  is  dated  in  1898.  In  the  same  year  E. 
DucRETET164  made  some  tests  in  France  using  an  "Oudin  resonator"  (in  its  essentials 
arranged  like  Fig.  212)  and  thereby  already  recognized  the  importance  of  tuning. 


176  WIRELESS  TELEGRAPHY 

(as  that  of  a  simple  antenna)  is  0.2  or  more.  Very  loose  coupling 
we  may  define  as  such  that  the  complications  discussed  in  Art.  58 
(two  frequencies  even  with  tuned  primary  and  secondary)  are  not 
noticeable.* 

a.  So  far  as  the  frequency  is  concerned,  the  primary  and  secondary  cir- 
cuits must  be  exactly  in  tune. 

b.  The  time  change  of  the  oscillations  in  the  aerial  is  similar  to  that 
shown  in  Fig.  123.     Only  one  oscillation  (i.e.,  one  frequency),  whose 
amplitude  first  increases  and  then  falls  off,  exists.     The  looser  the  coup- 
ling, the  more  nearly  the  rate  of  the  decrease  or  falling  off  of  the  amplitude  is 
that  which  would  be  obtained  with  an  oscillation  having  the  decrement  of  the 
condenser  circuit,  i.e.,  0.06  to  0.1. 

The  current  distribution  along  the  antenna  is  the  same  as  for  the  natural 
oscillations  of  the  antenna.  It  may  at  times  be  advantageous  to  so  shape 
the  current  distribution,  by  inserting  a  condenser,  as  to  bring  the  current 
anti-node  quite  high.  The  fact  that  this  reduces  the  degree  of  coupling 
between  the  primary  and  secondary  circuits  as  compared  to  having  the 
coupling  at  the  point  of  the  anti-node  of  current  [Art.  536]  is  not  detri- 
mental in  this  case. 

c.  Very  loose  coupling  is  used  when  it  is  essential  to  produce  very 
slightly  damped  oscillations.     In  practice,  however,  there  is  always  the 
accompanying  requirement  that  the  distance  effect  should  be  as  great  as 
possible  without  seriously  increasing  the  damping.     Now  from  Art.  88  it 
appears  that  the  current  effect  in  the  receiver  (circuit  III)  at  very  loose 
coupling  is  rapidly  increased  by  making  the  coupling  slightly  closer. 
Hence  for  good  distance  effect  it  is  important  to  make  the  degree  of 
coupling  as  high  as  the  sharpness  of  resonance  will  permit. 

106.  Coupled  Transmitter  for  Antennae  having  High  Damping.  Close 
Coupling. — When  the  greatest  possible  distance  effect  is  desired  with- 
out regard  to  high  damping,  close  couplingf  is  in  general  advantage- 
ous because  of  the  increased  current  amplitude  it  provides. 

a.  We  then  obtain,  whether  the  primary  circuit  is  in  tune  with  the 
antenna  or  not,  two  distinct  oscillations  of  different  frequency  and  hence 
[Art.  24]  different  current  distribution  along  the  antenna,  different  current 
amplitudes  at  the  current  anti-node  and  different  decrements.  As  a  mat- 
ter of  fact  the  primary  is  probably  always  tuned  to  the  secondary  circuit. 
Then,  from  Art.  58,  et.  seq.,  we  may  conclude:  the  oscillation  having 
the  higher  frequency  (shorter  wave-length)  has 

1.  A  greater  current  amplitude  at  the  anti-node  of  current. 

2.  More  favorable  current  distribution  along  the  antenna;  the  cur- 

*  That  is  K2  <  (dl2~^2)  2  [Art.  57]. 
f  That  is  K*>   (^F^-2)  2  [Art.  58]. 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


177 


rent  distribution  curve  for  a  simple  antenna  will  be  of  the  form  of  curve  /, 
Fig.  214,  for  the  shorter  wave  oscillation,  but  like  curve  II  for  the  longer 
wave  oscillation.  With  antennae  having  increased  end  capacity  the  two 
curves  are  not  much  different  from  each  other. 

3.  A  decrement  which  may  be  either  greater  or  less  than  that  of  the 
longer  wave  oscillation,  but  never  much  different  from  it. 

Hence  the  effect  upon  a  receiver  is  better,  in  fact  much  better  in  some 
respects,  if  the  receiver  is  tuned  for  the  oscillation  having  the  higher  frequency 
(shorter  wave-length). 

b.  Whether  it  is  best  to   tune   the  con- 
denser circuit  exactly  to  the  antenna  appears 
questionable    according    to    Art.   89.      It   is 
probable  that  a  better  effect  of  the  more  rapid 
oscillation   upon   a  receiver   is   obtained  by 
giving    the    condenser    circuit    a    frequency 
slightly  higher  than  that  which  the  antenna 
had  before  coupling.     The  author  does  not 
know  whether  this  has  been  tested  in  prac- 
tice.    An  increase  in  the  effect  of  more  than 
a  few  per  cent,  can,  however,  hardly  be  ex- 
pected, judging  from  the  laboratory  results. 

c.  According  to  Art.  88  the  current  effect 
in  a  receiver  (which  here  corresponds  to  the 
measuring  circuit)  tuned  to  the  higher  oscilla- 
tion, is  greatest  when  the  coupling  is  between 

4  per  cent,  and  10  per  cent.  However  in  Art.  88  the  tests  were  made 
with  a  condenser  circuit  as  secondary,  while  in  practice  we  have  an 
open  circuit  transmitter,  whose  current  distribution  must  be  considered. 
With  antennae  having  increased  end  capacity  this  can  make  but  little 
difference,  but  with  others,  the  current  distribution  for  the  more  rapid 
oscillation  is  improved  as  the  coupling  becomes  closer.  Hence  we  may 
conclude  that  a  fairly  close  coupling  is  advantageous  for  antennae.* 

d.  The  current  amplitude  at  the  anti-node  of  current  in  the  antenna, 
which  largely  determines  the  distance  effect,  is  given,  for  the  shorter 
wave  oscillation,  by  the  expression  [Art.  61a], 


FIG.  214. 


*  Widely  varying  degrees  of  coupling  have.  been  and  still  are  used  in  practice. 
The  TELEFUNKEN  Co.  formerly  used  up  to  10  per  cent,  coupling,  in  special  caseshaving 
obtained  excellent  results  with  much  higher  degrees  of  coupling.  The  Eiffel  Tower 
transmitter  operates  at  4.7  per  cent,  coupling.48  FLEMING1  states  the  usual  range  of 
coupling  to  be  from  30  per  cent,  to  70  per'  cent.  Presumably  the  degree  of  coupling  is 
of  very  little  importance  as  long  as  it  is  kept  over  a  certain  lower  limit.  It  would  seem 
as  if  the  worst  effects  of  very  close  coupling  are  compensated  by  the  resulting  advan- 
tages in  other  directions. 
12 


178  WIRELESS  TELEGRAPHY 

Hence,  the  frequency  (wave-length)  being  given,  it  is  advantageous  to 
use  antennae  having  large  effective  capacity.  Similarly  the  primary  cir- 
cuit should  have  as  large  capacity  as  possible,  compatible  with  the  avail- 
able energy.  A  limit  to  the  amount  of  capacity  is  encountered  in  that, 
with  a  given  frequency,  increasing  the  capacity  requires  a  reduction  in  the 
dimensions  of  the  current  path,  which  may  make  it  impossible  to  obtain  a 
sufficiently  high  degree  of  coupling.* 

This  same  reason  may  at  times  make  inductive  or  mixed  coupling 
necessary,  in  such  cases  where  it  is  impossible  to  make  pure  conductive 
coupling  sufficiently  close  without  sacrificing  the  advantages  of  large 
capacity. 

107.  Coupled  Transmitters  for  Slightly  Damped  Antennae. — a.  The 
case  of  very  loose  coupling  need  not  be  considered  for  antennas  whose  decre- 
ment is  less  than  0.1;  for  the  object  is  to  produce  oscillations  in  the  an- 
tenna which  have  not  the  high  damping  corresponding  to  the  natural 
oscillation  of  the  antenna,  but  the  low  damping  of  the  condenser  circuit. 
In  the  case  we  are  considering,  in  which  the  condenser  circuit  has  the 
same  or  only  slightly  lower  damping  than  the  antenna,  this  would  have 
no  practical  value. 

b.  The  effects  of  varied  degrees  of  coupling  are  qualitatively  the  same 
as  for  more  highly  damped  antennae.     The  tests  of  Art.  88,  conducted 
with  a  condenser  circuit  as  the  secondary,  indicate  that  6  per  cent,  is 
about  the  best  coupling  for  the  current  effect.     However,  for  antennae 
whose  current  distribution  varies  widely  at  different  points  it  must  be 
remembered  that  the  closer  the  coupling  is  made  the  more  advantageous 
for  good  distance  effect  does  the  current  distribution  become.     How 
much  this  factor  tends  to  displace  the  best  degree  of  coupling  is  a  question 
which  has  probably  not  been  answered  to  date  by  actual  tests. 

Practical  experience  seems  to  lead  to  the  conclusion  that  either  the 
degree  of  coupling  is  quite  immaterial  or  its  choice  depends  upon  the 
special  conditions  of  the  particular  case  to  such  an  extent,  that  no  generali- 
zations can  be  made.  The  TELEFUNKEN  Co.  reports  excellent  results 
with  a  60  per  cent,  coupling,  yet  this  same  company  used  a  4  per  cent, 
coupling  at  its  Nauen  high-power  station. 

c.  As  regards  the  kind  of  coupling  it  should  be  pointed  out  that  for 
umbrella  type  aerials  having  very  large  effective  capacity  the  direct 
(conductive)   connection  can  be  applied  even  for  very  close  coupling. 
This  can  be  made  clear  from  a  consideration  of  the  equation  [Art.  536] 

K 

: 

If  the  entire  condenser  circuit  is  used  for  the  coupling  and  the  coupling 

*  The  arrangements  which  F.  BRAUN165  has  devised  to  meet  this  condition,  under 
the  name  of  " Energieschaltungen"  (i.e.,  " energy  connections")  obviate  this  difficulty. 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS  179 

is  located  at  the  anti-node  of  current  in  the  antenna,  then  Z/i2  approxi- 
mately =  LI  and 


i.e.,  the  greater  the  effective  capacity,  C2,  of  the  antenna,  the  closer  will 
be  the  coupling. 

108.  Commercial  Form  of  the  Braun  Transmitter. — a.  Condensers. — 
The  requirements  of  the  condensers  used  are : 

1.  High  breakdown  resistance. 

2.  Small  volume,  convenient  form. 

3.  Low  energy  loss  due  to  dielectric  hysteresis. 

4.  No  brush  discharge. 

These  requirements  are  best  fulfilled  by  air,  particularly  compressed- 
air  condensers.  MARCONI  formerly  used  air  condensers  at  atmospheric 
pressure  at  the  Clifden  and  Glace  Bay  transatlantic  stations,  which  were 
equipped  with  a  tremendous  battery  of  air  condensers  totalling  1.6  mf., 
and  which  were  charged  to  a  potential  of  about  80,000  volts.  Compressed- 
air  condensers  of  the  form  shown  in  Figs.  68  and  69  have  been  in  use  by 
the  Nat.  Elec.  Sign.  Co.,  on  the  recommendation  of  FESSENDEN.  The 
disadvantage  of  air  condensers  lies  in  the  relatively  large  dimensions 
necessitated  by  the  low  dielectric  constant  of  air.  In  this  respect  con- 
densers of  good  flint  glass  are  preferable.  These  are  used  either  in  the 
form  of  plate  condensers,  which  are  submerged  in  oil  to  prevent  brush 
discharge  (DE  FOREST,  F.  DUCRETET,  E.  RoGER166  and  apparently  also 
now  in  use  by  MARCONI  in  his  transatlantic  stations),  or  else  in  the 
form  of  Ley  den  Jars  (the  battery  of  jars  shown  in  Fig.  70  is  part  of  a 
TELEFUNKEN  station  of  about  500  km.  range).  The  Eiffel  Tower  station 
has  Moscicki  condensers  [Art.  396]. 48 

In  order  to  minimize  the  brush  discharge  the  jars  are  sometimes 
(e.g.,  as  by  the  Nat.  El.  Sign.  Co.)  immersed  in  oil,  or  at  least  they  are  de- 
signed so  as  to  be  long  and  narrow  (Telefunken)  and  are  arranged  in 
series-parallel  combinations.  For  example,  the  Nauen  station  formerly 
had  three  batteries,  each  consisting  of  120  jars  in  parallel  (each  battery 
having  a  capacity  of  about  1.2  mf.),  joined  in  series  (Fig.  215). 

b.  As  to  the  design  of  the  current  path  of  the  condenser  circuit  it  is 
hardly  possible  to  make  any  general  statements.  Fig.  216  shows  a 
construction  of  the  TELEFUNKEN  Co.  As  formerly  used  for  a  station  of 
1000  km.  range,  it  was  made  of  silver-plated  copper  tubing,  some  of  the 
turns  being  joined  in  parallel. 

In  the  arrangements  illustrated  by  Figs.  211  and  212,  the  contacts 
A  and  B  are  made  so  as  to  be  movable,  allowing  a  convenient  adjustment 
of  the  frequency  and  the  coupling.  Needless  to  state,  the  current  path 


180 


WIRELESS  TELEGRAPHY 


should  be  so  designed  as  to  avoid  eddy  currents  in  the  condenser  coatings 
and  other  metallic  conductors  as  much  as  possible. 


c.  The  spark  gaps  may  have  either  stationary  or  rotating  electrodes. 

Gaps  with  stationary  electrodes  should  be  designed  with  as  large  a 

radius  of  curvature  as  possible  so  as  to  avoid  undue  heating.     The  ring- 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS  181 


FIG.  216. 


FIG.  217. 


182  WIRELESS  TELEGRAPHY 

shaped  electrodes  introduced  by  the  TELEFUNKEN  Co.  (Fig.  217),  have 
apparently  been  very  satisfactory.  Frequently  the  spark  gaps  are  en- 
closed in  a  case  so  as  to  reduce  the  terrific  noise  which  accompanies  the 
discharge  of  very  large  capacities  at  high  potentials.  Enclosing  the  gap 
furthermore  permits  the  use  of  gases  other  than  air  and  above  all  makes 
the  use  of  pressures  higher  than  atmospheric  possible.167 

In  regard  to  rotating  gaps  and  the  use  of  air  blowers  see  Art.  118. 

3.  QUENCHED  SPARK-GAP  TRANSMITTER.     WIEN'S  TRANSMITTER 

109.  Impulse  Excitation. — If  we  understand  this  term  as  covering  all 
those  methods  in  which  the  action  in  the  primary  exciting  circuit  lasts 
a  shorter  time  than  the  resulting  oscillations  in  the  secondary,  we  may 
distinguish  between  the  following  kinds  of  impulse  excitation. 

a.  Attention  to  one  method  has  already  been  called  in  Art.  5662. 
If  a  relatively  highly  damped  primary  circuit  is  caused  to  act  upon  a  less 
damped  secondary  circuit  very  loosely  coupled  to  it,  there  will  result  in 
the  secondary  not  only  an  oscillation  of  the  same  decrement  as  that  of 
the  primary  circuit,  but  also  one  having  the  lower  decrement  of  the  sec- 
ondary circuit.     This  latter  oscillation  continues  long  after  the  highly 
damped  primary  oscillations  have  disappeared. 

This  method,  at  one  time,  before  other  methods  of  impulse  excitation 
were  known,  was  proposed  (E.  NESPER121)  for  use  in  connection  with 
measurements.  It  should  not  come  into  question,  however,  in  radio- 
telegraph practice.  High  damping,  i.e.,  high  energy  consumption  in  the 
primary,  in  conjunction  with  .loose  coupling,  i.e.,  with  only  a  small  part 
of  the  energy  transferred  to  the  secondary  circuit,  must  necessarily  greatly 
reduce  the  efficiency. 

b.  The  quenched  gap  method  is  far  more  satisfactory.     Here,  after 
the  primary  circuit  has  had  the  opportunity  to  give  up  the  most  of  its 
energy  to  the  secondary,  the  oscillations  in  the  primary  are  quenched. 
The  principle  of  this  method  was  discussed  in  Art.  62  et  seq.,  its  practical 
application  in  Art.  Ill   et  seq. 

c.  Regarding  a  kind  of  mechanical  quenching  by  means  of  a  rotating 
spark  gap  see  Art.  1186  and  d. 

d.  An  impulse  excitation  in  the  true  sense  of  the  word  is  represented  in 
Figs.  218  and  219.     If  the  circuit  from  the  cell  E  is  first  closed  and  then 
abruptly  opened  by  means  of  the  interrupter  A,  the  resulting  current 
curve  will  be  about  like  that  marked  /  in  Fig.  220.     This  will  produce  an 
e.m.f.  of  the  form  of  E  in  Fig.  220,  in  the  coil  S.     The  current  resulting 
from  this  e.m.f.  charges  the  condenser,  C,  which  discharges  in  its  natural 
period  (G.  EicHHORN168).     Hence,  while  with  the  quenched  gap  method 
we  have  regular  oscillations  in  the  primary  which  are  quenched  fairly 
rapidly,  we  have  in  this  case  of  true  impulse  excitation,  an  aperiodic 
action  which  produces  the  oscillations  in  the  secondary. 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


183 


The  advantages  of  this  method  for  measuring  purposes  have  already 
been  pointed  out  in  Art.  78d.  A  good  interrupter  is  of  course  essential; 
those  having  the  contact  fastened  to  a  stretched  string  or  wire  which  is 
vibrated  by  an  electromagnet  are  well  suited  to  the  purpose.* 

A  practical  application  of  this  method  is  in  the  form  of  the  so-called 


LfiflfiM 


E 


FIG.  219. 


"station-testers,"  condenser  circuits  of  adjustable  frequency,  which  can  be 
made  to  oscillate  with  the  aid  of  very  low  amplitudes. 

Fig.  221  illustrates  one  of  these  as  made  by  the  TELEFTJNKEH  Co.  The 
connections  are  those  of  Fig.  218.  The  "make  and  break"  of  the  direct 
current  is  accomplished  by  an  interrupter  (at  the  right  of  Fig.  221)  similar 
to  the  ordinary  electric  bell  or  buzzer.  Frequently  wave  meters,  as  for 
instance  that  of  C.  LORENZ  and  the  newer  type  of  the 
TELEFUNKEN  Co.,  are  arranged  for  use  as  "station-testers" 
also. 

e.  Pure  impulse  excitation  (as  described  in  d)  or  else  a 
condition  lying  between  the  cases  of  the  quenched  spark 
gap  and  pure  impulse  excitation  can  also  be  obtained  with 
a  condenser  circuit  as  primary,  if  its  oscillations  disappear        FIG.  220. 
at  the  first  passage  through  zero  or  at  least  after  a  very 
few  oscillations.    This  condition  obtains  under  certain  circumstances  with 
hydrogen  spark  gaps  (B.  GLATZEL169)  and  especially  with  unsymmetrical 
gaps,f  also  to  some  extent  with  mercury  arc  lamps,  in  fact  even  when  the 
condenser  circuit  is  not  coupled  to  any  secondary  circuit.     The  quench- 
ing of  the  spark  therefore  is  not   dependent   on   the   reaction    of  the 
secondary. 

*  These  are  made  especially  for  this  method  by  the  TELEFUNKEN  Co.,  C.  LORENZ 
and  ROB.  W.  PAUL  (New  Southgate,  London). 

t  S.  EiSENSTEiN170  heated  cathode,  cold  anode;  L.  E.  CHAFFEE — aluminium  cath- 
ode, copper  anode  in  hydrogen,  also  at  times  with  gaps  having  symmetrical  elec- 
trodes.93 


184 


WIRELESS  TELEGRAPHY 


Furthermore,  in  this  case  the  occurrence  of  pure  quenching  action  is  of 
course  independent  of  the  degree  of  coupling.  The  latter  may  be  made  as 
high  as  the  arrangement  of  the  circuits  permits. 


FIG.  221. 

E.  L.  CnAFFEE2  has  succeeded  in  obtaining  continuous  oscillations  with 
such  a  gap,*  in  fact  even  with  a  frequency  of  about  3  X  106  per  sec. 

(X  =  about  100  m.).  For  this  purpose 
he  so  regulates  his  primary  circuit  and 
his  current  supply  that  after  say  three 
cycles  of  the  secondary  oscillations  there 
is  a  discharge  of  the  primary  circuit. 
The  first  primary  discharge  excites  the 
secondary  oscillations,  which  fall  off 
slightly  during  the  next  two  cycles,  but 
are  given  a  new  impulse  in  the  third 
period  at  the  right  instant  (in  phase). 

110.  The  Connections. — a.  These  are 
in  general  the  same  for  the  WIEN  trans- 
mitter (Fig.  222)  as  for  the  BRAUN 
transmitter.  The  antenna  is  coupled 
either  inductively  or  conductively  with 
the  condenser  circuit  containing  the  quenched  gap.171 

But  the  degree  of  coupling,  while  it  may  be  chosen  between  wide  limits 

*  R.  C.  GALLETTi1700  seems  to  have  obtained  the  same  result  by  means  of  a  peculiar 
combination  of  a  number  of  condenser  circuits  and  spark  gaps  which  act  successively 
one  after  another. 


FIG.  222. 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


185 


with  the  BRATJN  transmitter,  must  in  the  case  of  the  Wien  transmitter  be 
adjusted  as  nearly  as  possible  to  the  critical  degree  of  the  particular  spark 
gap  in  question  in  order  to  obtain  the  maximum  efficiency.  For  good 
quenched  spark  gaps  this  critical  value  is  usually  about  20  per  cent.* 

In  order  to  obviate  the  necessity  of  varying  the  degree  of  coupling 
whenever  the  wave-length  is  changed,  the  TELEFUNKEN  Co.  has  devised 
the  following  arrangement  (Fig.  223) :  In  the  condenser  circuit  there  is 
placed  a  coil,  LI,  of  much  greater  self-induction  than  the  rest  of  the 
primary  circuit.  This  coil  is  used  for  a  direct  coupling  of  the  antenna. 


FIG.  223. 


FIG.  224. 


The  wave-length  is  changed  by  varying  the  coefficient  of  self-induction  of 
this  coil  (which  in  the  actual  construction  is  in  the  form  of  a  Rendahl 
variometer),  and  the  tuning  of  the  antenna  to  the  primary  circuit  is 
effected  by  means  of  the  special  tuning  coil  L2. 

Under  these  conditions  the  coefficient  of  coupling  remains  constant 
and  independent  of  the  wave-length.     We  have 


'LiZ* 

as  after  tuning  CiLi  must  =  C2L2  [Arts.  3  and  27]. 

As  a  matter  of  fact,  it  is  advisable  to  make  the  coupling  somewhat 
looser  for  the  shorter  waves.  For  this  purpose  an  additional  coil,  Lf 
(Fig.  224) ,  which  is  not  used  for  the  coupling  and  whose  self-induction  is 
of  no  consequence  for  the  long  waves  (Li  being  very  large)  but  comes 

*  In  Art.  646  it  was  brought  out  that  some  quenched  gaps  have  several  critical 
couplings.  That  one  which  gives  the  greatest  current  effect  in  the  secondary  is  of 
course  chosen.  With  the  gaps  described  in  Art.  109,  the  coupling  may  be  increased 
far  above  20  per  cent.,  in  fact  to  40  per  cent,  or  even  higher.  So  far,  however,  it  has 
not  been  demonstrated  that  this  has  resulted  in  higher  efficiencies  than  have  been 
obtained  with  ordinary  quenched  gaps. 


186 


WIRELESS  TELEGRAPHY 


into  importance  for  the  shorter  waves  (Li  relatively  small),  is  inserted 
in  the  primary  circuit. 

b.  The  oscillations  sent  off  into  space  are  virtually  the  natural  oscil- 
lations of  the  antenna.  Their  damping  should  be  kept  as  low  as  possible 
to  secure  sharp  resonance  in  the  receiver.  Accordingly  it  is  universal 
practice  to  use  antennae  with  greatly  decreased  radiation  damping  [Art. 
98]  and  make  provision  for  reducing  their  losses  as  much  as  possible  in 
order  to  maintain  a  good  efficiency  for  the  antenna  [Art.  99]. 

If  it  were  desired  to  use  antennae  with  strong  radiation  and  the  attend- 
ant high  radiation  damping  and  yet  keep  the  damping  of  the  oscilla- 
tions radiated  into  space  fairly  low,  this  could  only  be  accomplished  by 


FIG.  225. 


means  of  the  arrangement  shown  in  Fig.  225.  The  primary  quenched 
gap  circuit,  /,  is  coupled  to  a  very  weakly  damped  condenser  circuit 
(the  "intermediate  circuit"  //)  which  in  turn  acts  inductively  upon  the 
antenna  through  a  very  loose  coupling.  The  relation  between  the  inter- 
mediate circuit,  II,  and  the  antenna,  ///,  is  the  same  as  for  a  loosely 
coupled  BRAUN  transmitter  [Art.  105],  so  that  the  oscillations  of  the 
antenna  can  be  made  to  have  the  same  low  damping  as  the  intermediate 
circuit. 

The  intermediate  circuit,  which  adds  a  material  complication  to  the 
equipment,  has  been  dropped  in  radio  practice.160  It  has  been  found 
preferable  to  secure  low  damping  for  the  radiated  oscillations  by  reducing 
the  damping  of  the  antenna  itself.  An  intermediate  circuit  would  then 
be  of  value  only  if  its  decrement  were  much  less  than  0.05,  say  at  least 
0.01-0.005.  This  to  be  sure  can  be  attained  in  the  laboratory,  but  hardly 
in  practical  installations. 

111.  Practical  Construction  of  Quenched  Spark  Gaps. — Their  short 
life  stands  in  the  way  of  the  commercial  use  of  the  mercury  arc  lamp  and 
the  quenching  tubes  mentioned  in  Art.  63,  unless  some  more  durable 
form  be  devised  in  the  future.  Such  quenched  spark  gaps  as  have 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


187 


found  application  in  practice  (some  however  only  for  a  short  time),  have 
all  belonged  to  the  class  of  very  short  metallic  gaps. 

Some  of  these  spark  gaps — a  number  of  them  have  been  called  "high 
frequency  generators" — were  believed  by  their  inventors,  who  worked 
with  a  very  high  spark  frequency,  to  produce  undamped  oscillations. 
As  a  matter  of  fact,  however,  under  the  actual  working  conditions  these 
gaps  all  acted  as  quenched  spark  gaps. 


FIG.  227. 


FIG.  228. 


a.  The   gap    made  by   the    Badische    Anilin  und    Sodafabrik    (VON 
KocH172)  has  two  concentric  metal  electrodes  (Figs.  226,  227),  very  close 
together,  between  which  a  whirling  eddy  of  air  is  blown. 

This  eddy  is  obtained  by  blowing  the  air  into  the  cylindrical  or  con- 
ical space  between  the  two  electrodes  tangentially,  as  shown  diagrammat- 
ically  for  a  simple  case  in  Fig.  228.  This  whirling  of  the  air  has  the 
following  advantages: 

1.  Intensive  cooling  of  the  electrodes. 

2.  The  spark  is  blown  about  all  over  the  elec- 
trode so  that  the  discharge  is  constantly  taking 
place  at  new  spots,  not  heated  by  the  preceding 
discharge.     Hence  we  obtain  in  this  way  much 
the  same  advantages  as  are  obtained  with  ro- 
tating   electrodes,   viz.,   regularity   of  the   dis- 
charge,   increased     breakdown    potential     and 
thereby  increased  energy. 

3.  The  spark  gap  is  rapidly  deionized,  thereby 

raising  the  breakdown  potential  and  preventing  the  formation  of  arcs. 

Ordinary  fans  or  blowers  generally  are  not  sufficient  for  increasing 
the  quenching  action  (H.  RAUSS);  the  air  velocities  obtained,  unless  very 
special  means  are  employed,  are  not  great  enough  to  renew  the  air  fully 
in  the  short  time  available  for  deionization  [see  Art.  656].  To  be  sure, 
the  use  of  extremely  powerful  blowers  makes  it  possible  to  materially 
increase  the  quenching  action  and  also  to  obtain  quenching  in  gaps 
several  millimeters  long,  under  conditions  which  without  a  blower  would 
give  rise  to  the  different  coupling  waves  (B.  GLATZEL,  PicnoN173). 

b.  In  the  "plate  spark  gap"174'  devised  by  E.  v.  LEPEL175  the  electrodes 


FIG.  229. 


188 


WIRELESS  TELEGRAPHY 


are  two  metallic  plates  having  a  very  narrow  and  finely  adjustable  space 
between  them.     They  are  separated  by  a  paper  ring  (Fig.  229)  made  of 


FIG.  230. 


FIG.  232. 


carefully  chosen  material.  The  spark  which  passes  over  the  gap  in  the 
space  left  open  by  the  hole  in  the  paper  ring,  tends  to  choose  points  along 
the  edge  of  the  paper,  which  is  gradually  burned  away  by  the  spark. 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


189 


Presumably  the  paper  provides  against  the  non-passage  or  at  least  the 
irregular  passage  of  the  spark,  which  would  otherwise  result  with  the  low 


JL* 


FIG.  233. 

potentials  (sometimes  only  220  volts,  D.C.)  used  by  v.  LEPEL.  Fig. 
230  illustrates  the  exterior  construction  of  one  of  these  gaps  as  arranged 
for  water  cooling. 

c.  Particular  credit  is  due  the  TELE- 
FUNKEN  Co.176  for  its  work  in  the  construc- 
tive development  of  the  quenched  plate 
gaps.  Its  gap,  a  diagrammatic  cross-sec- 
tion of  which  is  shown  in  Fig.  231,  has 
electrodes  of  silver-plated  copper.  Be- 
tween the  rims  of  these  plates  is  a  mica 
ring  which  serves  both  as  an  insulator  and 
an  air  seal.  The  widened  space  AA,  is 
intended  to  prevent  the  spark  from  dis- 
charging at  the  rim  of  the  mica  ring. 
The  distance  between  the  faces  of  the  elec- 
trodes is  very  small,  about  0.2  mm. 

As    only    a    comparatively    very    low 


FIG.  234. 


FIG.  235. 


voltage,  and  hence  low  energy  in  the  individual  oscillations,  can  be  ap- 
plied in  view  of  the  shortness  of  the  gap,  the  TELEFUNKEN  Co.  always 
uses  a  number,  say  10  or  12  of  the  gap  elements  or  sections  shown  in 
Fig.  231,  joined  in  series,  so  as  to  form  "series  spark  gaps"  (Fig.  232). 


190 


WIRELESS  TELEGRAPHY 


Excellent  results  have  been  obtained  with  these  quenched  gaps.  Nor 
is  it  surprising  that  this  form  of  gap  should  offer  such  advantages.  The 
plate  gap  probably  provides  the  most  favorable  conditions  of  all  quenched 
spark  gaps,  certainly  of  all  those  employing  stationary  electrodes,  As 
the  ions  are  emitted  from  the  metallic  circuit,  they  always  find  themselves 


FIG.  236, 

in  the  immediate  vicinity  of  a  conducting  surface  toward  which  they  are 
driven  either  by  absorption  or  by  the  action  of  the  electric  field  existing 
between  the  gaps.  Consequently  the  degree  of  coupling  may  be  brought 
as^high  as  say  20  per  cent,  even  with  relatively  large  amounts  of  energy  and 
thereby  a  high  efficiency  can  be  attained. 

These  gaps  moreover  have  the  great  practical  advantage  of  requiring 
hardly  any  attention  or  re-adjustment.     The  spark  moves  about  over  the 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


191 


surface  of  the  electrode  so  that  the  latter  is  worn  down  very  evenly  and 
very  slowly.     Hence  it  need  be  cleaned  only  at  very  long  intervals.     The 


FIG.  237. 

series  of  gaps,  moreover,  offers  a  simple  and  convenient  method  of  varying 
the  radiated  energy;  to  reduce  this  simply  requires  the  short-circuiting  of 


192  WIRELESS  TELEGRAPHY 

one  or  more  of  the  individual  gaps — as  may  be  necessary,  for  instance, 
when  suddenly  called  upon  to  work  with  a  much  nearer  receiving  station. 

d.  The  gap  made  by  C.  LORENZ  (O.  ScHELLER177)  (Fig.  233)  instead  of 
having  flat  plates,  consists  of  two  concentric  or  almost  concentric  spherical 
surfaces.     In  this  construction  the  gap  length  is  practically  the  same  at  all 
points. 

e.  The  gap  devised  by  W.  PEUCKERT178  also  belongs  to  the  plate-gap 
class,  differing  from  the  others  in  that  at  least  one  of  the  two  electrodes  is 
rotated. 

Two  forms  of  this  gap  are  shown  in  Figs.  234  and  235.  In  the  former 
the  plates,  A  and  B,  are  vertical.  One  of  these,  A,  is  stationary,  and 
through  this  oil  is  kept  flowing,  which  then  spreads  out  in  the  space 
between  the  two  plates.  In  the  second  form  (Fig.  235)  the  plates  are  in  a 
horizontal  plane.  An  atmosphere  containing  hydrogen  between  the 
plates  is  procured  by  allowing  alcohol  to  drip  from  a  holder  on  top  into  the 
gap.  The  Peuckert  gap,  which  for  a  short  time  was  made  by  the  so-called 
Polyfrequenz-Elektrizitatsgesellschaft,  is  distinguished  by  great  regu- 
larity of  the  oscillations. 

112.  Commercial  Construction  of  the  Wien  Transmitter. — a.  Figs. 
236,  237  and  238  illustrate  three  quenched  spark-gap  stations  of  the  Tele- 
funken  Co.179  The  explanation*  given  below  for  Fig.  236  is  probably 

*  2.  =40  amp.  D.C.  fuses. 

3.  =  D.C.  switch. 

4.  =  Voltmeter  switch. 

5.  =  Voltmeter— 250  volts. 

6.  =  Motor  starter. 

7.  =  Field  rheostat  (motor). 

8.  =4  HP,  110  volts,  1500  r.p.m.,  D.C.  motor. 
10.1 

11.  f  =  High  frequency  protective  devices  (condensers). 

12.  J 

13.  =  2  kw.,  250  volts,  500  cycles.     Alternator. 

15.  =  Slide  rheostat  for  alternator  field. 

16.  =  30  amp.  A.C.  fuses. 

17.  =  A.C.  switch. 

18.  =  A.C.  ammeter,  50  amp. 

20.  =  Key. 

21.  =  Choke  coil  for  main  supply  circuit. 

22.  =  220/8000  volts  transformer. 

23.  =  Quenched  spark  gap — 8  sections. 

24.  =  Primary  capacity  27  X  10~3  MF. 

25.  =  Primary  self-induction. 

26.  =  Aerial  hot-wire  ammeter,  20  amp. 
28.  =  Aerial  variometer. 

30.  =  Antenna  shortening  capacity. 

33.  =  Receiver. 

34.  =  Primary  transformer  coil  of  receiver., 
42.  =  Telephone. 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


193 


sufficient  for  an  understanding  of  the  other  two  figures.     The  simplicity 
of  these  stations  is  at  once  evident.     One  need  only  compare  Fig.  238, 


illustrating  the  quenched  gap  transmitter  of  the  Nauen  high-power  station 
with  the  former  BRAUN  transmitter  (Fig.  215)  of  the  same  station  to  appre- 


13 


194 


WIRELESS  TELEGRAPHY 


ciate  this.  This  simplicity  of  quenched  gap  sets  is  made  possible  by  the 
comparatively  low  potentials,  e.g.,  8000  volts  in  the  2  kw.  station  shown 
in  Fig.  236,  which  can  be  used;  this  removes  the  necessity  of  connecting 
the  condensers  in  series.  In  fact  the  use  of  the  extremely  convenient 
mica  or  paper  condensers  has  become  possible.  The  one  disadvantage  of 
these  last-named  condensers,  namely,  their  high  energy  dissipation,  does 
not  come  into  question  so  much  here  as  it  does  in  the  case  of  the  BRAUN 
transmitter.  For,  as  the  oscillations  of  the  primary  circuit  are  quenched 
after  the  first  few  cycles,  it  is  not  so  serious  that  the  condensers  consume 
somewhat  more  energy  per  cycle,  particularly  as  this  loss  is  very  small  in 
comparison  to  that  in  the  gap.  Nevertheless,  as  long  as  there  are  no 
special  limitations  to  the  space  available,  good  Ley  den  jars,  air  or  oil  con- 
densers are  always  given  preference  in  order  to  keep  the  efficiency  as  high 
as  possible;  and  this  can  usually  be  done,  as  the  moderate  potential  makes 
it  possible  to  keep  the  dimensions  of  such  condensers  comparatively  small. 
b.  The  circuit  connections  have  already  been  discussed  in  Art.  110; 
they  are  probably  as  shown  in  Fig.  224  in  most  cases.  When  changing  of 
the  wave-length  between  wide  limits  is  desired,  this  is  frequently  obtained 
by  inserting  a  condenser  (the  smallbattery  of  Leyden  jars  marked  30,  in 
Fig.  236)  directly  in  the  antenna  for  the  shorter  waves  and  connecting  it  in 
parallel  to  an  inductive  coil  in  the  antenna  for  the  longer  waves  [Art.  98c]. 

4.  GENERAL  CONSIDERATION  OF  TRANSMITTERS  OF  DAMPED 

OSCILLATIONS 

113.  Operation  by  Means  of  Interrupted  Direct  Current. — The  use  of 

spark  coils  (induction  coils)  operated  by  inter- 
rupted direct  current  is  quite  frequent  in  small 
stations. 

The  induction  coil  must  be  able  to  give  a 
relatively  large  amount  of  electricity  at 
moderate  potential  rather  than  very  high 
potential.  The  requirements  are  therefore 
quite  different  from  those  for  the  operation  of 
X-ray  (ROENTGEN)  tubes. 

The  usual  electromagnetic  interrupter  suf- 
fices for  small  currents.  It  is  economical  of 
both  room  and  energy,  and  hence  continues 
to  be  used  for  small  portable  sets  and  air- 
ships, and  also  for  quenched  gap  transmitters 
on  shipboard  as  shown  in  Fig.  237  (particu- 
larly in  the  form  of  emergency  equipment, 
operated  from  a  storage  battery),  in  which 
case  however  a  higher  frequency  of  the  interruptions  is  required. 

For  larger  currents  the  mercury  turbine  interrupters  have  given  good 


FIG.  239. 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


195 


service.  Fig.  239  shows  one  of  these  as  made  by  the  Allgemeine  Elek- 
trizitatsgesellschaft.  The  advantages  of  the  mercury  turbine  interrupter, 
particularly  for  use  in  measurements,  are:  1.  It  interrupts  relatively 
large  currents  with  great  regularity;  2.  the  speed  of  the  motor  and  hence 
the  frequency  of  the  interruptions  are  independent  of  the  amount  of 
current  to  be  broken. 

114.  Alternating-Current  Operation. — The  disadvantage  of  induction 
coils  with  interrupted  direct  current  lies  mainly  in  the  difficulty  of  ob- 
taining sufficient  quantities  of  electricity  to  charge  large  condensers  to  a 
high  potential.  The  use  of  alternating-current  and  commercial  trans- 
former designs  at  once  suggests  itself.  A.C.  operation  differs  according 
to  whether 

1.  Ordinary  spark  gaps  (BRAUN  transmitter)  or 

2.  Quenched  spark  gaps  (WiEN  transmitter) 
are  used. 

a.  In  the  first  case  (BRAUN),  where  in  general  very  high  potentials  are 
used,  if  we  were  simply  to  connect  the  primary  (low-tension  side)  of  the 
transformer  to  the  generator  and  the  secondary  (high-tension  side) 
across  the  spark  gap,  the  following  difficulties  would  result: 


FIG.  240. 

1.  The  A.C.  transformer  would  continue  to  deliver  current  after  the 
oscillations  in  the  primary  circuit  had  died  out.     That  leads  to  the  forma- 
tion of  arcs,  which  heat  the  electrodes,  ionize  the  gap  for  an  unnecessarily 
long  time,  thereby   lowering  the  breakdown  potential   and  the  initial 
amplitude  of  the  oscillations. 

2.  The  high-tension  side  of  the  transformer  is  almost  short-circuited 
by  the  spark.     This  may  damage  the  winding  and  also  cause  a  disad- 
vantageous reaction  upon  the  primary  of  the  transformer  (low-tension 
side). 

This  second  difficulty  can  be  overcome,  at  least  in  part,  by  inserting 
condensers  (dC2  Fig.  240)*  or  choke  coils  in  the  leads  from  the  trans- 

*  The  connections  shown  in  Fig.  240  are  those  formerly  used  in  the  Marconi 
Station  at  Poldhu. 


196 


WIRELESS  TELEGRAPHY 


former  secondary  to  the  spark  gap,  also  by  placing  sufficiently  large  choke 
coils  in  the  primary  side  ($2,  Fig.  240)  of  the  transformer. 

AS  to  the  first-named  difficulty,  much  depends  upon  whether  a  very 
high  discharge  frequency — e.g.,  500  to  2000  per  second  for  "tone  trans- 
mitters"— or  a  low  frequency,  say  5  to  25  per  second,  is  used.  With  the 


FIG.  241. 

higher  frequencies,  the  use  of  rotating  spark  gaps  [see  Art.  118&]  is  probably 
not  feasible,  if  the  energy  handled  is  large. 

With  the  low  frequencies,  the  various  operating  difficulties  can  be 
very  ingeniously  overcome  by  the  arrangement98  employed  by  the  TELE- 
FUNKEN  Co.  under  the  name  of  "resonance  inductor"  or  "resonance 
transformer." 


Spark 

FIG.  242. 

The  transformer  (or  induction  coil)  has  an  open  core;  its  terminals  are 
connected  to  the  condenser  circuit  in  the  usual  manner  (Fig.  241).  The 
spark  gap,  E,  is  so  adjusted  in  length  that  the  normal  secondary  potential 
is  far  below  that  necessary  to  jump  across  the  gap.  We  then  have  the 
case  discussed  in  Arts.  67  and  68:  an  undamped  oscillating  primary 
circuit  (armature  of  the  alternator,  coil  D,  and  primary  coil,  Si,  of  the 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


197 


resonance  transformer)  coupled  to  a  condenser  circuit  (secondary  coil, 
$2,  of  the  resonance  transformer  and  ABCDE).  If  these  two  circuits 
are  adjusted  so  as  to  be  in  resonance,  then  the  oscillations  which  result 
upon  completing  the  primary  current  path,  will  be  about  as  shown  in  Fig. 
242.  The  current  amplitude  and  hence  also  the  potential  amplitude  in- 
crease with  each  cycle,  the  potential  rising  far  above  the  normal  value 
which  would  correspond  to  the  ratio  of  the  transformer,  until,  after  a 
number  of  periods,  a  spark  jumps  across  the  gap,  F,  thereby  causing  the 
condenser  circuit  FABCDEF  to  oscillate  rapidly. 

Due  to  these  oscillations,  the  energy  which  has  been  accumulated 
in  the  condenser  circuit  S^ABCDE,  is  quickly  consumed.  Consequently 
there  is  a  rapid  fall  in  potential,  no  arc  is  formed  and  there  is  no  great 
increase  in  the  primary  current. 


FIG.  243. 


This  series  of  events  then  repeats  itself,  beginning  with  the  next 
period.  No  spark  occurs  until,  after  a  number  of  cycles,  sufficient  energy 
has  been  pumped  [Art.  61c]  into  the  secondary  circuit  (S^ABCDE)  to 
bring  the  potential  to  the  necessary  amplitude. 

The  advantages  of  this  method  are,  therefore:  avoiding  of  arcs  and  of 
short-circuiting  of  the  secondary  coil,  low  spark  frequency  and  much 
higher  voltage  than  would  correspond  to  the  transformer  ratio.* 

*  With  an  initial  frequency  of  fifty  cycles  per  second  the  spark  frequency,  if  so  de- 
sired, can  easily  be  reduced  to  five  per  second  and  the  secondary  potential  raised  to 
three  times  the  normal  transformation  value. 


198  WIRELESS  TELEGRAPHY 

For  a  given  transformer  and  at  a  given  frequency  there  is  a  best  degree 
of  coupling.  In  order  that  this  may  be  secured,  it  is  advisable  to  introduce 
adjustable  inductive  coils  (D,  Fig.  241)  in  the  primary  (or  secondary) 
circuit  or  to  use  a  BOAS  resonance  transformer  (Fig.  243)  *  so  as  to  allow 
variation  of  the  coupling  between  the  primary  and  secondary  circuits. 

In  the  Telefunken  Station  at  Nauen  (Fig.  215)  which  formerly  was 
operated  with  a  resonance  transformer,  the  high  potential  was  obtained 
by  means  of  four  transformers  in  parallel  (right  front  of  Fig.  215).  Two 
inductive  coils  (left  front  of  Fig.  215)  were  placed  in  the  primary  circuit. 

6.  With  quenched  spark  gaps  (WiEN  transmitter)  the  deionization  of 
the  gap  [Art.  65]  is  so  intense  that  the  danger  of  the  formation  of  arcs  is 
far  less  than  with  ordinary  gaps.  Hence  with  quenched  gaps  there  is 
nothing  to  prevent  the  use  of  A.C.  generators  and  transformers,  nor  of 
machines  for  tone  transmission,  whose  frequency  is  between  250  and  1000 
cycles  per  second. 

It  is  advisable  to  so  regulate  the  current  that  at  most  two  or  three  par- 
tial discharges,  preferably  only  one  takes  place  during  each  half  period.176 
With  several  partial  discharges  the  tone  in  the  receiving  telephone  [Art. 
165]  is  apt  to  lose  all  its  purity.  And  while  a  flute-like  tone  free  from 
upper  harmonics  has  no  special  advantage  (in  fact  a  tone  having  some 
pure  upper  harmonics  seems  to  be  better  for  receiving180),  an  impure  dis- 
cordant tone,  as  produced  by  numerous  irregular  partial  discharges  is 
certainly  not  favorable  for  good  results.  Moreover  such  irregular,  partial 
discharges  tend  to  weaken  rather  than  strengthen  the  effect  upon  the  tele- 
phone diaphragm,  as  it  may  often  not  have  time  to  return  to  its  posi- 
tion of  equilibrium  and  in  any  case  is  forced  into  extremely  complex 
movements. 

If  the  current  is  further  weakened,  the  same  effect  as  is  obtained  with 
a  resonance  transformer  can  be  secured,  a  spark  passing  only  every  second 
or  third  half  period;  the  tone  heard  in  the  receiver  is  then  at  the  corre- 
spondingly lower  octaves. 

c.  One  danger  to  which  the  alternator,  and,  under  certain  conditions, 
also  the  motor  driving  it  are  subjected,  consists  in  the  high  frequency  cur- 
rents induced  in  the  leads  by  the  primary  circuit  or  antenna  currents. 
These  may  produce  very  high  potentials  endangering  the  insulation.  To 
counteract  this  as  much  as  possible  it  is  customary  to  connect  condensers 
(those  marked  10,  11,  12  in  Fig.  236)  or  sometimes  non-inductive  resist- 
ances (incandescent  lamps)  in  parallel  with  the  motor  and  generator. 

115.  Direct-current  Operation. — a.  Direct  current  at  high  potential 
may  also  be  used  in  the  supply  circuit  for  charging  the  condensers,  espe- 
cially when  quenched  spark  gaps  are  used.  The  arrangement  for  these 
conditions  is  very  simple  (Fig.  244).  The  quenched  gap  circuit,  /,  is 
connected  to  the  D.C.  generator  through  series  resistance,  RQ,  and  induc- 

*  These  are  particularly  recommended  for  measuring  purposes. 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


199 


tance,  Lo.  If  the  voltage,  the  gap  length  and  the  supply  current  are 
properly  adjusted  with  respect  to  one  another,  instead  of  an  arc  resulting 
across  the  gap  electrodes  we  obtain  a  varying  potential  like  that  illustrated 
in  Fig.  291  (lower  part).  The  direct  current  charges  the  condensers  and 
their  potential  rises  until  the  breakdown  potential  of  the  gap,  F,  is 
reached.  Then  the  potential  falls  through  a  series  of  oscillations  reaching 
zero  or  almost  zero,  whereupon  the  process  repeats  itself.  The  number  of 
discharges  per  unit  of  time  depends  upon  the  size  of  the  supply  current,  as 
this  determines  the  time  necessary  for  bringing  the  condensers  to  the 
breakdown  voltage  of  the  gap.  The  discharge  frequency  can  accordingly 


FIG.  244. 

be  varied  between  wide  limits  by  regulation  of  the  current  supply.  In 
order  to  secure  regularity  of  the  discharges,  it  is  important  to  bring  the 
voltage  up  as  high  as  possible,  at  any  rate  not  lower  than  1000  volts. 

The  series  resistance  in  the  supply  circuit  should  preferably  have  a 
rapidly  rising  characteristic.  The  Nernst  resistances,  consisting  of  iron 
wires  in  a  glass  bulb  filled  with  hydrogen,  are  particularly  well  suited  to 
this  purpose;  metal  filament  lamps  may  also  be  used. 

b.  The  inductance,  L0,  should  be  wound  without  iron ;  if  for  any  reason 
an  iron  core  is  desired,  it  is  advisable  to  keep  the  magnetization  above  the 
saturation  point. 

The  effects  of  the  self -inductance  are  as  follows:181 

1.  It  greatly  reduces  the  fluctuations  of  the  supply  current. 

2.  The  maximum  gap  potential  is  greatly  increased  by  the  inductance, 
at  times  even  rising  considerably  above  the  dynamo  potential.* 

3.  The  increased  maximum  potential  improves  the  irregularity  of  the 
discharges  and,  finally, 

4.  The  series  resistance,  and  hence  the  energy  consumed  in  the  supply 
circuit,  can  be  less  than  would  be  required  without  the  self-inductance, 
without  endangering  the  generator. 

c.  The  supply  source  is  usually  a  D.C.  generator  several  of  these  being 
connected  in  series  if  necessary.     In  the  Marconi  transatlantic  stations 

*  In  the  transatlantic  Marconi  stations  (Fig.  255),  the  actual  maximum  gap 
potential,  with  12,000  volts  normal  generated  (storage  battery)  potential,  is  stated  to 
be  about  18,000  volts.191  This  is  apt  to  be  dangerous  for  the  generator.  See  Art, 
114c  for  methods  of  protection  against  this. 


200  WIRELESS  TELEGRAPHY 

at  Clifden  and  Glace  Bay,  a  storage  battery  of  6000  cells,  corresponding  to 
a  potential  of  about  12,000  volts  (see  Fig.  255),  is  in  parallel  with  the 
dynamos  or  can  also  be  used  alone. 

116.  Measurement  of  the  Energy  Supplied;  Determination  of  the 
Efficiency. — To  measure  the  efficiency  of  a  radio  transmitter,  it  is  neces- 
sary to  find  the  energy  used  in  the  secondary  circuit  on  the  one  hand  and 
that  supplied  by  the  current  source  to  th.e  primary  circuit  on  the  other. 
a.  Measurement  of  Energy  Consumed  in  the  Secondary  Circuit. — If  the 
kind  of  secondary  circuit  is  optional,  it  is  advisable  to  choose  a  condenser 
circuit  and  to  determine  its  effective  resistance,  R,  by  measuring  the 
decrement  [Art.  77,  et  seq.].  It  may  be  well  to  construct  the  current  path 
of  braided  conductors  having  individually  insulated  wires  and  to  insert  in 
this  a  resistance,  R,  of  very  fine  constantan  wire  (special  resistance 
material)  which  has  the  same  resistance  for  oscillating  as  for  direct  cur- 
rents [see  Art.  366]  and  which  should  be  so  large  that  the  resistance  of  the 
rest  of  the  current  path  becomes  negligible  in  comparison.  If  a  hot-wire 
ammeter  is  then  inserted  in  the  secondary  circuit  and  /22e//  is  measured, 
then  Rl^e/f  is  very  nearly  equal  to  the  energy  consumed  per  second  in  the 
secondary  circuit.  If  the  indications  of  the  hot-wire  meter  are  not  con- 
sidered reliable,  the  resistance  can  be  placed  in  an  insulated  (against  heat) 
vessel,  filled,  say,  with  oil  and  the  heat  developed  measured  calometric- 
ally,71  from  which  the  energy  consumption  per  second  in  the  secondary 
circuit  may  be  determined. 

If  the  secondary  circuit  is  an  antenna,  the  current  effect,  /22 «//,  is 
measured  by  means  of  an  ammeter  inserted  in  the  antenna  and  the  re- 
sistance, R,  of  the  antenna  is  measured  by  one  of  the  methods  given  in 
Art.  1006.  Then  the  product  RIZ2 «//  =  the  energy  consumed  per  second 
in  the  antenna. 

6.  Measurement  of  the  Energy  Supply. 

1.  In  the  case  of  low  discharge  frequency,  as,  e.g.,  with  a  Braun  transmitter 
when  operated  by  an  influence  machine,  an  induction  coil  with  D.C.  in- 
terrupter or  a  resonance  transformer,  the  amount  of  energy  supplied  is 
found  as  follows:  if  V  =  the  discharge  potential  and  C  =  the  capacity 
of  the  condenser,  then  the  energy  in  the  condenser  at  the  instant  just  pre- 
vious to  its  discharge  is  H  CV2.  If  now  there  are  f  discharges  per  second, 
it  follows  that  the  energy  which  the  condenser  receives  from  the  supply 
circuit  in  each  second  must  be  f  .%CV2.*  The  discharge  voltage,  for 
slow  (static)  charging  of  the  condensers,  can  be  determined  by  means  of  a 
suitable  electrometer,182  or  from  Table  VI  if  the  spark-gap  electrodes  are 
spherical.  This,  however,  applies  only  if  the  discharge  potential  is  the 
same  with  a  static  charge  as  under  operating  conditions;  this  condition 

*  The  assumption  is  that  the  condenser  actually  gives  up  its  entire  charge.  If 
the  condenser  coatings  after  the  discharge  still  retain  a  difference  in  potential,  Vi 
(residual  charge),  then  the  energy  supplied  per  second  is  f .  %C(V2~  7i2). 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


201 


can   be   approximated   by  projecting   ultra-violet  light   upon  the  gap 
electrodes  and  using  a  very  low  spark  frequency. 

2.  With  a  high  discharge  frequency  it  can  not  be  assumed  in  general 
that  the  discharge  potential  is  the  same  as  the  breakdown  potential  ac- 
quired by  means  of  a  static  charge.  In  this  case,  if  the  discharge  poten- 
tial is  not  too  high,  the  energy  supplied  to  the  primary  circuit  can  be  meas- 
ured by  an  electrodynamic  wattmeter  connected  either  at  the  point  W  or 
W  (Fig.  245),  according  to  whether  or  not  the  energy  consumed  in  the 
series  resistances  and  inductances  is  to  be  included. 


W 


FIG.  245. 


As  the  frequency  of  the  supply  current  is  usually  much  higher  than  that 
of  commercial  alternating  currents  and  as  its  form  is  far  from  being  sinu- 
soidal, the  ordinary  commercial  wattmeters  are  not  to  be  recommended 
for  this  purpose.  They  generally  possess  phase  errors  which,  at  the 
lower  commercial  frequencies,  approximately  sinusoidal  currents  and 
not  too  great  a  phase  displacement  between  current  and  voltage,  can 
be  roughly  corrected  for  by  means  of  compensating  coils  of  some  sort, 
but  which  otherwise  may  become  quite  considerable.  Hence,  we  are 
limited  to  the  use  of  special  wattmeters183  in  which  such  errors  are  care- 
fully avoided,  unless  it  is  preferred  to  use  a  laboratory  wattmeter, 
consisting  of  a  fixed  current  coil  in  which  is  suspended  a  potential  coil, 
very  small  compared  to  the  current  coil,  made  of  very  fine  wire  and  carry- 
ing a  small  mirror  attached  to  it.  The  suspension  and  current  lead  are 
best  made  of  a  bronze  strip,  while  a  telescope  and  scale  serve  for  reading 
the  deflection.  The  usual  commercial  wattmeter  multipliers  (series  re- 
sistances are  not  suitable,  as  they  are  not  free  from  capacity  and  self-in- 
duction; incandescent  lamps*  or  liquid  resistances!  may  be  used. 

3.  Another  method  is  based  upon  the  use  of  the  quadrant  electrometer. 
A  known  resistance,  R  (Fig.  246)  which  must  have  practically  no  induc- 
tance or  capacity  and  be  independent  of  the  frequency  (e.g.,  a  straight, 
thin  constantan  wire,  placed  in  a  quartz  tube  filled  with  oil  for  cooling)  is 
inserted  in  the  supply  circuit,  and  across  its  ends,  P  and  Q,  the  two  quad- 

*  But  they  must  be  used  far  below  the  point  of  incandescence. 

t  e.g.,  the  special  boracic  acid — mannite  resistances  of  MAGNANINI,  with  platinum 
electrodes  as  large  as  possible.  Formula:  1500 g.  water,  181  g.  mannite,  62  g.  boracic 
acid;  to  this  add  a  little  potassium  chloride,  the  quantity  being  such  as  to  give  the 
resistance  a  very  slight  temperature  coefficient. 


202 


WIRELESS  TELEGRAPHY 


rant  pairs,  aaf  and  bb'  of  the  electrometer  are  connected.     The  needle  is 
joined  to  T  (Fig.  246). 

Then  the  theory184  will  show  that  the  deflection  of  the  needle, 


The  proportionality  factor,  a,  of  the  instrument  having  been  de- 
termined by  calibration  with  static  potentials  and  the  current  effect  J2e// 
by  an  ammeter  /  connected  in  the  circuit,  then  from  the  deflection,  #,  we 


Electrometer 


To 
Generator 


obtain  the  energy  consumption  per  second  between  the  points  Q  and  T, 
and  hence  the  energy  supplied  per  second  to  the  condenser  circuit/. 

117.  The  Key. — a.  Just  as  in  ordinary  wire  telegraphy,  keys  are  used 
for  telegraphing.  In  radio  work,  however,  the  difficulty  of  breaking  cir- 
cuits carrying  heavy  currents  and  having  high  self-induction  presents  it- 
self. This  may  at  times  give  rise  to  large  sparks,  which  rapidly  destroy 
the  key  contacts. 


FIG.  247. 

These  sparks  can  be  reduced  by  not  entirely  breaking  the  current 
path.  This,  for  instance,  is  done  in  the  arrangement  of  Fig.  240  in  which 
closing  the  key  short-circuits  the  inductive  coil,  Si,  and  opening  the  key 
again  causes  the  full  current  to  flow  through  Si;  in  short  the  current  is 
alternately  increased  and  decreased,  but  never  entirely  broken.  This 
method  can  be  reversed  by  leaving  the  inductance,  in  circuit  (Fig.  241) 
and  short-circuiting  the  primary  side  of  the  transformer  with  each  closing 
of  the  key.185 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS  203 

A  simple  solution  of  the  difficulty  for  moderately  large  currents  is  the 
construction  (shown  diagrammatically  in  Fig.  247)  formerly  used  by  the 
TELEFUNKEN  Co.  and  the  MARCONI  Co.,  as  designed  by  F.  BRATJN  and 

A.  GRAY,  respectively.* 

Underneath  the  key  proper  (i.e.,  the  lever  arm  of  the  key)  a  spring,  F, 
is  placed,  to  which  an  iron  armature,  E,  and  a  platinum  contact,  Ci,  are 
attached.  If  the  key  and  hence  the  spring,  F,  are  pressed  down,  contact  Ci 
touches  contact  C2  and  the  path  of  the  primary  current  of  the  induction 
coil  or  transformer,  as  the  case  may  be,  is  completed.  The  current  passes 
not  merely  through  the  key,  along  the  route  AFCiC2,  but  then  also  flows 
through  the  winding  S.  If  now  the  key  is  released  so  as  to  move  upward, 
contact  Ci  will  nevertheless  remain  touching  C2,  as  the  magnetic  action  due 
to  the  current  in  S  continues  to  hold  down  the  armature  E  and  hence  the 
spring  with  the  contact  C\.  Not  before  the  primary  current  has  become 
reduced  to  virtually  zero,  is  the  armature  and  hence  the  contact  Ci  re- 
leased from  Czj  at  which  time  of  course  no  spark  is  formed. 

b.  In  large  stations  "key  relays"  are  probably  always  used.     An 
ordinary  key,  manipulated  by  hand,  closes  an  auxiliary  circuit  which 
(similarly  to  the  remote  control  switches  used  for  commercial  high-tension 
work)  operates  the  key  or  contactor  opening  the  main  circuit.     The  con- 
struction of  good  key  relays,  or  "  relay  keys,"  as  they  are  sometimes  called, 
is  by  no  means  a  simple  matter,  owing  to  the  very  rapid  and  frequent 
interruption  of  heavy  current  demanded  in  telegraph  service. 

c.  Where  extremely  rapid  operation  is  required,  as,  e.g.,  in  the  Wheat- 
stone  rapid  method,  automatic  keys  can  be  used. 

The  principle  of  these  is  essentially  as  follows :  The  message  is  punched 
in  telegraph  code  into  a  strip  or  tape  of  strong  paper  or  other  insulating 
material.  For  instance,  the  letter  a  would 
appear  as  in  Fig.  248.  The  strip  so  formed 
is  then  pulled  between  the  contacts  of  a  key 
suitably  designed,  thereby  completing  the 

circuit  as  each  perforation  passes  through  the  key.  The  actual  con- 
struction of  such  rapid  telegraph  apparatus  and  automatic  keys  is 
usually  very  complicated.186 

118.  Spark  Gaps  with  Rotating  Electrodes. — -,a.  In  gaps  having 
smooth  electrodes,  as  in  the  MARCONI  gap  shown  in  Fig.  249,  the  spark, 
which  always  chooses  the  shortest  or  approximately  shortest  path  through 
the  air,  will  constantly  jump  across  from  different  points  of  the  electrodes, 

B,  A  and  5'.f     This  prevents  harmful  local  heating  of  the  electrodes, 
which  heating,  with  fixed  electrodes,  tends   to   reduce  the  breakdown 
voltage  of  the  gap  and  causes  a  rapid  deterioration  of  the  electrodes 

*  These  designs  of  the  key  also  prevent  the  formation  of  very  high  potentials 
at  the  sudden  breaking  of  the  current. 

t  A  is  a  very  rapidly  revolving  disc,  while  B  and  B'  rotate  slowly. 


204 


WIRELESS  TELEGRAPHY 


and  consequent  irregularities  in  the  oscillations.  Furthermore,  the  air 
currents  caused  by  the  rotation  assist  the  deionization  of  the  spark  gap 
and  the  cooling  of  the  electrodes.  In  the  spark  gaps  of  F.  DUCRETET 

and  E.  RoGER188  (Fig.  250)  which  have 
a  tube,  C,  as  one  electrode  and  a  rotating 
sphere,  S,  as  the  other,  a  special  strong 
air  current  is  provided  by  the  ventilator 
{*,  or  blower,  V.  The  advantage  of  such 
provisions  becomes  more  evident  as  the 
spark  frequency  and  the  current  are  in- 
creased, i.e.,  as  the  tendency  to  form  arcs 
increases. 

b.  The  action  of  spark  gaps  having 
small  projections  on  the  electrodes  as, 
e.g.,  that  shown  in  Fig.  251  (R.  FESSEN- 
DEN,  NAT.  ELEC.  SIG.  Co.)  or  in  Fig. 

252  (MARCONI  Co.189)  depends  largely  upon  the  shortest  distance  be- 
tween the  electrodes,  their  width  and  their  velocity.  Let  us  first 
assume  that  the  minimum  distance  between  the  electrodes  is  such  that 


Bo 


FIG.  250. 


the  highest  potential  occurring  across  the  gap  will  be  just  sufficient  to 
create  a  spark  discharge.     Then 

1.  With  moderate  speed  and  moderate  width  of  the  electrodes,  the  gap 
will  have  the  advantage,  for  A.C.  operation,  of  good  cooling  of  the  elec- 
trodes and  the  prevention  of  arcs,  for  the  gap  length  grows  so  rapidly 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


205 


206 


WIRELESS  TELEGRAPHY 


after  the  oscillations  have  died  out  that  there  is  no  opportunity  for  an 
arc  formation.  In  this  case  then,  the  spark  gap  is  mounted  directly  on 
the  shaft  of  the  alternator  (Fig.  251)  or  of  a  synchronous  motor  and  the 
number  and  location  of  the  projections  or  sparking  points  so  chosen  that 

they  are  nearest  together  (minimum  gap 
length)  at  the  instant  when  the  A.C. 
voltage  is  at  its  maximum. 

With  D.C.  operation  a  gap  of  this 
type  secures  regularity  of  the  dis- 
charges, the  frequency  being  regulated 
by  the  speed  control  of  the  driving 
motor.  If  this  frequency  is  high 
enough  an  audible  sound  or  tone  (tone 
transmitter)  is  obtained  in  the  receiving 
telephone. 

2.  If  the  electrodes  are  very  narrow 
and  their  speed  very  high,  the  result 

may  be  as  follows:  The  oscillations  of  the  condenser  circuit  commence 
at  just  about  the  instant  when  the  electrodes  are  closest  together.  While 
the  oscillations  continue,  the  gap  length  increases  very  rapidly.  At  the 
same  time  the  potential  amplitude  in  the  condenser  circuit,  if  coupled  at 
all  closely  to  a  secondary  circuit,  rapidly  falls  off  [Art.  59c].  The  effect 
of  both  these  factors,  i.e.,  increasing  gap  length  and  decreasing  potential, 


FIG.  252. 


FIG   253. 

may  be  to  disrupt  the  spark  after  a  very  few  periods,  even  in  such  cases 
where,  if  the  electrodes  remained  stationary,  the  spark  would  not  be  auto- 
matically quenched  after  half  a  cycle.  (This  is  sometimes  referred  to  as 
"mechanical  quenching.") 

Whether  or  not  a  mechanical  quenching  results,  depends  largely  upon 
the  velocity,  the  wave-length  and  the  coupling  [Art.  59c]  used.     If  the 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS 


207 


peripheral  velocity  of  the  electrodes  is  taken  at  200  m.  per  second 
(a  speed  which  is  obtainable  [see  d]),  and  a  5  per  cent,  coupling  employed 
so  that  the  potential  amplitude  in  the  primary  circuit  will  be  zero  or 
nearly  zero  after  ten  periods  of  the  oscillations,  then  the  movable  elec- 
trode will  in  this  time  have  covered  a  distance  of  2  cm.  with  a  wave- 
length of  3000  m.,  and  a  distance  of  4.4  cm.  with  a  wave-length  of  6700 
If  the  gap  is  properly  constructed,  however,  the  distance  between  the 


m. 


HHHHHHHHHHH 

Storage  J3attery 
-  Inductance 


FIG.  254. 


FIG.  255. 


electrodes  will  have  become  so  large  by  that  time  that  there  is  very  little 
chance  for  the  spark  to  form  again  during  the  next  few  periods,  particularly 
if  the  minimum  gap  length  is  very  small. 

In  all  cases  the  effect  of  increasing  the  gap  length  is  assisted  by  the 
strong  air  currents  formed.  In  order  to  fully  take  advantage  of  this, 
spark  gaps  with  rotating  electrodes  have  been  constructed  in  the  form  of 
actual  ventilators  (Fig.  253,  Balsillie  System190). 

c.  Another  possible  case  consists  in  having  the  gap  length  less  than 
the  length  which  the  potential  used  can  just  jump  across  (Fig.  254, 
"short -circuit  spark  gap")  and  to  revolve  the  electrode  projections  at 
very  high  speed.  When  a  projection  of  the  rapidly  rotating  electrode, 
F,  approaching  the  stationary  or  slowly  rotating  electrodes  FI  and  F2, 
comes  sufficiently  close,  a  discharge  takes  place.  While  this  discharge 
is  occurring  the  electrodes  come  nearer  together  and  the  gap  length,  the 

*  MARCONI'S  transatlantic  stations  [d]. 


208  WIRELESS  TELEGRAPHY 

gap  resistance  and  the  energy  consumption  are  reduced  to  very  low  values 
[Art.  lid].  Such  spark  gaps  combine  the  two  advantages  of  compara- 
tively high  initial  voltage  with  a  relatively  short  average  gap  length  and 
a  very  short  gap  length  at  the  time  when  the  oscillations  of  the  discharge 
have  already  become  very  low  in  amplitude.  The  best  results  are  ob- 
tained, other  things  being  equal,  with  the  highest  speeds  and,  for  a  given 
speed,  with  the  greatest  retardation  of  the  discharge  [Art.  426].  Ac- 
cordingly ultra-violet  light  is  to  be  avoided  as  much  as  possible. 

d.  The  spark  gap  shown  in  Fig.  255,  which  is  use  d  in  the  transatlantic 
MARCONI  stations  at  Clifden  and  Glace  Bay,191  is  a  combination  of  a 
short-circuit  gap  and  a  mechanically  quenched  gap.  The  electrode  pro- 
jections on  the  wheel  F  are  so  shaped  that  the  gap  between  the  discs  FI 
and  F2  is  very  small  only  while  there  is  a  projection  between  the  two  discs. 
On  the  other  hand,  the  peripheral  velocity  of  F  is  so  great  (about  200 
m.  per  second),  the  degree  of  coupling  so  low — it  is  reported  as  being 
approximately  5  per  cent. — and  the  width  of  the  projections  is  so  meas- 
ured, that  the  spark  is  disrupted  after  half  a  cycle  and  does  not  again 
form  until  the  next  projection  comes  into  play. 

The  discharge  retardation  seems  to  be  used  to  excellent  advantage 
in  these  gaps;  at  a  potential  of  15,000  volts  and  a  frequency  of  45,000 
cycles  per  sec.  (X  =  6700  m.)  it  is  claimed  that  the  spark  occurs  only  about 
one  period  before  the  instant  at  which  the  projections  of  F  are  at  their 
minimum  distance  from  the  discs  FI  and  F2.  The  result  of  this  short 
spark  gap  combined  with  the  heavy  current  due  to  the  relatively  high 
discharge  voltage  and  capacity,  is  a  very  low  energy  consumption  in  the 
primary  condenser  circuit.  The  total  decrement  of  the  primary  circuit, 
when  not  coupled  to  the  secondary,  is  claimed  to  be  only  about  0.03  to 
0.06.* 

6.  COMPARISON  OF  THE  DIFFERENT  TYPES  OF  TRANSMITTERS 

119.  Difference  between  the  Coupled  and  the  Simple  (MARCONI) 
Transmitter. — a.  That  the  coupled  transmitters  are  more  complicated 
and  that  it  costs  more  to  construct  them  is  self-evident.  In  addition,  a 
relatively  small  induction  coil  with  mechanical  interrupter  and  a  few  stor- 
age battery  cells  usually  suffices  for  a  simple  transmitter  with  its  low 
capacity;  the  operating  costs  are  therefore  exceedingly  low.  Hence,  if 
only  comparatively  short  distances f  are  to  be  covered  in  telegraphing 
and  if  it  is  important  to  keep  the  energy  consumptionf  as  low  as  possible, 

*  The  equivalent  resistance  of  the  entire  condenser  circuit  with  its  spark  gap  is 
given  in  one  case  as  0.022  ohm. 

t  Ranges  of  100-150  km.,  with  masts  about  30  m.  high  have  been  attained,  with 
the  simple  MARCONI  transmitter. 

|  e.g.,  stations  which  are  difficult  of  access  or  light  portable  sets  (such  as  light- 
ship stations  or  portable  military  stations). 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS  209 

the  simple  MARCONI  transmitter  offers  great  advantages,  which  in  fact 
have  caused  it  to  be  retained  in  use  to  the  present  day  and  which  will 
perhaps  keep  it  in  use  for  quite  some  time  to  come  as  an  emergency 
transmitter. 

b.  But  it  is  in  relation  to  the  question  of  energy  that  the  simple 
MARCONI  transmitter  is  at  its  greatest  disadvantage.     To  be  sure,  it 
does  not  require  much  energy,  but  the  only  way  in  which  the  energy  can 
be  increased  is  by  raising  the  initial  voltage  (see  e).     On  the  other  hand, 
it  is  possible  to  radiate  much  greater  quantities  of  energy  in  the  form  of 
electromagnetic  waves  from  a  coupled  transmitter,  in  view  of  the  large 
capacity  available  in  the  primary  circuit,  than  from  a  simple  MARCONI 
transmitter  at  the  same  potential. 

Closely  related  to  this  is  another  advantage  of  the  coupled  trans- 
mitter, viz.,  the  oscillations  can  be  so  modified,  one  may  say,  so  formed, 
as  to  be  best  adapted  for  a  particular  receiver.  If  it  is  important  to  have 
great  amplitude  for  the  waves  emanated,  this  can  be  secured  without 
bringing  the  damping  so  high  as  to  be  prohibitive.  Again,  if  very  low 
damping  is  desired,  this  also  can  be  obtained  without  causing  too,  great 
a  reduction  in  the  amplitude  of  the  wave.  It  is  for  these  reasons  that  in 
the  one  extreme  case,  where  the  greatest  range  is  the  object,  as  well  as 
in  the  other,  where  the  sharpest  possible  tuning  is  the  desideratum, 
coupled  transmitters  are  always  used. 

c.  As  regards  the  energy  losses  it  should  be  borne  in  mind  that  in  the 
simple  MARCONI  transmitter,  the  spark  gap  lies  in  the  antenna,  while  in 
the  coupled  transmitter  the  gap  is  transferred  to  the  condenser  circuit. 
As  to   which  is   the  preferable  location   depends   upon   the   particular 
circumstances. 

One  thing  is  certain:  when  the  object  in  view  is  to  radiate  oscillations 
having  the  lowest  possible  decrement  from  a  given  antenna,  the  coupled, 
and  above  all,  the  WIEN  transmitter  is  far  superior  to  the  simple  MARCONI 
transmitter.  In  both  cases,  with  the  simple  as  with  the  WIEN  transmit- 
ter, we  obtain  practically  the  natural  oscillations  of  the  antenna;  but 
in  the  case  of  the  simple  transmitter,  the  spark  decrement,  which  in 
itself  is  about  as  large  as  that  of  a  weakly  radiating  antenna  having 
no  spark  gap,  is  added  to  the  decrement  of  the  antenna  of  the  WIEN 
transmitter. 

d.  The  additional  advantage  of  BRAUN'S  coupled  transmitter  is  that 
the  upper  partial  oscillations  of  the  antenna  are  not  produced  with  an 
appreciable  amplitude.     This  energy  loss  is  therefore  not  involved.     But 
in  the  BRATJN  transmitter,  at  least  when  closely  coupled,  a  second  wave  is 
obtained,  which  consumes  energy,  but  is  of  no  value  for  the  distance 
effect  in  the  customary  receiving  arrangements. 

e.  A  further  material  advantage  of  the  coupled  transmitter  lies  in  the 
fact  that  the  antenna  is  charged,  not  directly  by  the  induction  coil  or 

14 


210  WIRELESS  TELEGRAPHY 

transformer,  as  is  the  case  with  the  simple  transmitter,  but  only  by  the 
oscillations.  The  result  is  that  the  insulation  of  the  antenna  becomes  a 
much  simpler  problem  and  that  when  slight  faults  occur  in  the  insulation 
these  have  but  little  effect  upon  the  oscillations  [Art.  43].  In  the  simple 
transmitter,  the  slightest  defect  in  the  insulation  suffices  to  endanger  the 
entire  operation. 

There  is  a  natural  tendency  to  belittle  this  last  element  and  to  assume 
that  good  successful  insulation  can  present  no  serious  technical  difficulties. 
The  fact  remains  that  insulation  troubles,  especially  in  the  tropics,  are 
often  so  great,  that  they  have  caused  the  failure  of  entire  installations192 
[see  Art.  126]. 

120.  Comparison  of  the  Braun  and  Wien  Transmitters. — a.  The  main 
advantages  of  the  WIEN  transmitter  as  compared  to  the  BRAUN  trans- 
mitter are  as  follows : 

1.  In  the  BRAUN  transmitter  the  oscillations  and  hence  the  energy  con- 
sumption in  the  primary  circuit  last  as  long  as  in  the  secondary.  In  the 
Wien  transmitter  they  last  only  for  a  few  periods. 

2.,  The  BRAUN  transmitter  produces  two  waves  in  practice,  of  which 
only  one  is  fully  made  use  of  in  the  receiver.  The  WIEN  transmitter 
emits  practically  only  one  wave  from  its  antenna  [Art.  78c]. 

As  regards  this  second  point  it  is  of  course  possible  to  prevent  the 
formation  of  two  waves  by  means  of  very  loose  coupling  [Art.  105],  but 
then  the  transfer  of  energy  to  the  secondary  circuit  becomes  very  ineffi- 
cient. The  former  frequent  practice  of  making  the  coupling  just  suffi- 
ciently loose  to  make  the  two  coupling  waves  only  slightly  different  in 
their  wave-length,  is  of  little  or  no  use.  The  two  coupling  waves  in  that 
case  act  upon  the  receiver  like  a  single  wave  of  much  higher  damping, 
which  makes  the  advantage  of  the  coupled  transmitter  more  or  less 
illusory. 

As  to  the  first  point,  this  would  absolutely  fix  the  superiority  of  the 
WIEN  transmitter,  so  far  as  efficiency  is  concerned,  if  the  same  potentials 
and  the  same  spark  gap  were  used  in  the  BRAUN  and  WIEN  transmitters. 
But,  as  a  matter  of  fact,  a  relatively  long  spark  gap,  with  resultant  low 
gap  decrement  [Art.  lid],  is  used  in  the  BRAUN  transmitter,  while  either 
low  potentials  and  short  gaps  or  high  potentials  and  a  series  of  gaps^'.e., 
in  either  case,  a  high  gap  decrement  [Arts,  lid  and  12]  are  used  in  the 
WIEN  transmitter.  Hence  the  energy  consumed  per  cycle  is  much  greater 
in  the  WIEN  than  in  the  BRAUN  transmitter,  so  that  the  total  energy  loss 
in  the  gap  circuit  of  the  WIEN  transmitter  may  be  quite  considerable  in 
spite  of  the  short  duration  of  the  oscillations.* 

*  This  no  doubt  is  also  why  it  is  so  important  to  have  the  coupling  in  the  WIEN 
transmitter  as  close  as  possible,  thereby  minimizing  the  duration  of  the  primary 
oscillations,  without,  however,  making  the  coupling  so  close  as  to  impair  the  quench- 
ing action. 


TRANSMITTERS  OF  DAMPED  OSCILLATIONS  211 

Nevertheless  the  modern  WIEN  transmitters  seem  to  be  much  more 
efficient  than  the  old  BRAUN  transmitters.*  But  in  acknowledging  this 
it  must  be  remembered  that  formerly  fundamental  principles  in  the  con- 
struction were  often  disregarded  either  for  the  sake  of  convenience  or  for 
other  specific  reasons;  some  of  the  old  transmitters  actually  appear  as  if 
they  had  been  intended  not  merely  for  telegraphing,  but  also  for  warming 
the  room  in  which  they  were  located  by  the  heat  developed  by  the  eddy 
currents.  In  the  meantime  experience  has  taught  the  necessity  of 
applying  the  principles  discovered  in  the  laboratory  to  commercial  sta- 
tions so  as  to  minimize  all  losses  of  energy.  Hence  we  should  not  compare 
an  old,  poorly  constructed  BRAUN  transmitter  with  a  new,  WIEN  trans- 
mitter designed  and  constructed  with  the  proper  care. 

It  is  readily  conceivable  that  the  mechanically  quenched  gaps  should 
have  high  efficiency,  as  the  use  of  long  sparks  and  therefore  low  gap  decre- 
ments is  here  possible.  In  any  case,  MARCONI'S  combination  of  mechan- 
ical quenching  with  short-circuiting  the  gap  must  be  very  efficient,  for  it 
unites  good  quenching  action191  with  low  energy  consumption  in  the  con- 
denser circuit. 

Quenching  tubes  also  permit  the  use  of  long  sparks  with  low  gap  decre- 
ments. Their  use  can  give  very  good  efficiency — M.  WiEN92  obtained 
80-60  per  cent,  efficiency  (ratio  of  secondary  to  primary  energy)  at  30,000- 
80,000  volts  primary — although  the  energy  loss  in  the  tube  is  added  to 
that  in  the  spark. 

b.  The  use  of  high  initial  voltages  and  long  sparks  in  the  BRAUN 
transmitter  is  not  accidental.  Nor  does  the  reason  lie  solely  in  the  lower 
decrements  of  the  long  sparks-.  For  in  the  BRAUN  transmitter,  of  the  two 
possible  methods  of  increasing  the  energy  of  the  transmitter  (i.e.,  increas- 
ing either  the  initial  voltage  or  the  spark  frequency)  only  the  former  can  be 
done  in  a  simple  way,  the  latter  involving  considerable  difficulties.  If 
the  gap  has  stationary  electrodes,  then,  even  with  such  large  dimensions 
as  belong  to  the  spark  gap  shown  in  Fig.  217,  local  heating  of  the  elec- 
trodes, with  all  its  attendant  disadvantages  (arcs,  reduced  breakdown 
potential),  is  unavoidable,  if  the  spark  frequency  is  brought  to  the  region 
of  1000  cycles  per  sec.  The  use  of  rotating  electrodes,  however,  is  in- 

*  COUNT  ARCOIGO  claims  that  the  efficiency  (energy  of  the  secondary  divided  by 
the  primary  energy)  of  the  TELEFUNKEN  quenched  gap  transmitters  is  about  85  per 
cent.193 

M.  WiEN17  obtained  the  following  figures  from  a  very  carefully  designed  BRAUN 
transmitter  at  an  initial  potential  of  72,000  volts:  di  =  0.034,  d2  =  0.175,  K'  =  0.032, 
77  =  82  per  cent,  and  for  di  =  0.034,  <22  =  0.087,  K'  =  0.024,  rj  =  66  per  cent. 
(i)  =  efficiency).  Such  high  efficiency,  however,  is  attained  only  by  the  most  careful 
construction  of  the  primary  circuit;  as  soon  as  WIEN  replaced  the  compressed  gas 
condensers  he  was  using  by  MOSCICKI  condensers,  the  efficiency  dropped  from  about 
80  to  about  69  per  cent.  The  efficiency  of  the  BRAUN  transmitters  which  were  used 
in  practice  was  much  lower. 


212  WIRELESS  TELEGRAPHY 

herently  a  complication,  so  that  this  means  is  hardly  apt  to  be  chosen 
except  for  large  stations  [see  Art.  114a]. 

In  the  WIEN  transmitter  these  conditions  are  more  favorable.  Here 
the  oscillations  in  the  primary  circuit  are  only  of  very  brief  duration,  so 
that  the  heat  developed  in  the  gap,  at  the  same  .current  amplitude,  is  much 
less.  Furthermore  the  deionization  of  this  type  of  gap  is  in  itself  so 
rapid,  that  there  is  but  little  tendency  to  form  an  arc.  Hence,  the  use 
of  high  discharge  frequencies  involves  no  difficulties  in  the  Wien  trans- 
mitter [see  Art.  1146],  and  the  result,  namely,  a  high,  pure  note  in  the  re- 
ceiving telephone  and  a  lowering  of  the  antenna  potential,  thereby  reducing 
insulation  difficulties,  has  proven  its  value  in  daily  practice. 

c.  In  the  WIEN  transmitter,  there  is  an  important  advantage,  particu- 
larly for  portable  stations,  in  conjunction  with  the  short  duration  of  the 
primary  oscillations,  namely,  the  possibility  of  using  condensers  made  of 
mica  or  similar  dielectrics.  The  doing  away  of  the  series  connection 
means  a  general  simplification,  not  only  for  portable  sets,  but  for  all  other 
stations  as  well  [see  Art.  112a]. 

The  brush  discharge  on  the  condensers,  which  is  very  harmful  in  the 
BRAUN  transmitter  and  necessitates  undesirable  complications  [Art.  108a], 
is  of  no  importance  in  the  WIEN  transmitter. 


CHAPTER  VIII 
HIGH  FREQUENCY  MACHINES  FOR  UNDAMPED  OSCILLATIONS 

121.  The  Alexanderson-Fessenden  Machines. — It  is  reasonable  to 
expect,  a  priori,  that  undamped  oscillations  of  high  frequency  can  be 
generated  by  a  machine  in  the  same  way  that  commercial  alternating 
currents  of  lower  frequencies  are  produced.  But  it  is  an  exceedingly 
difficult  problem  when  frequencies  of  the  order  of  105  cycles  per  sec.  are  to 
be  obtained.  First  of  all,  at  these  high  frequencies,  the  hysteresis  and  eddy 
current  losses  become  very  large;  a  radical  attempt  to  prevent  the  former 
by  building  machines  without  iron  was  soon  abandoned  as  impractical. 
Then  the  structural  difficulties  increase  very  rapidly  as  the  frequency  is 
raised.  Assume  that  a  frequency  of  105  cycles  per  sec.  is  obtained  at  the 
maximum  allowable  speed  of  20,000  r.p.m.;*  then  if  the  diameter  of  the 
rotor  is  305  mm.,t  a  path  of  only  3.2  mm.  remains  for  the  generation  of 
each  cycle,  that  is,  3.2  mm.  is  the  maximum  width  available  for  a  pair  of 
armature  coils  with  their  insulation.  And  if  this  width  is  not  to  be 
further  reduced,  a  high  speed  is  unavoidable,  thereby  involving  the  well- 
known  mechanical  difficulties  attendant  upon  rotation  at  such  velocities. 

In  spite  of  these  difficulties,  N.  TESLA'S  early  efforts  in  this  direction 
have  been  renewed  again  and  again,  particularly  in  America,194  where 
FESSENDEN  devoted  himself  to  the  problem.  The  high  frequency  alter- 
nators which  through  his  influence  were  built  for  the  NAT.  ELEC.  SIG. 
Co.,  by  the  GENERAL  ELECTRIC  Co.  from  E.  F.  W.  ALEXANDERsoN's195 
designs,  probably  represent  the  best  which  has  been  achieved  in  this  field 
of  work  in  the  past. 

a.  The  100,000  cycle  ALEXANDERSON  alternator  (A  =  3000  m.)  is  of 
the  inductor  type. 

Fig.  256  is  a  diagrammatic  cross-section  of  one  of  these  alternators. 
The  excitation  is  obtained  by  means  of  a  single  large  field  coil,  S,  which  is 
wound  around  the  entire  machine  and  is  supplied  with  direct  current. 
The  magnetic  flux  lines,  M ,  of  this  coil  pass  through  the  iron  cores,  E\  and 
Ez,  of  the  small  armature  coils,  Si  and  *S2.  The  only  movable  part,  Ji,  has 
teeth  or  projections,  Z,  of  iron,  at  its  periphery.  When  one  of  these  teeth 
is  just  between  the  armature  coils,  Si  and  $2,  the  magnetic  flux,  M,  has 
a  path  almost  entirely  through  iron,  excepting  only  at  the  very  small  air 
gaps  between  the  teeth,  Z,  and  the  cores,  Ei  and  E2;  in  this  position  then, 

*  Speed  of  ALEXANDERSON'S  machine  at  a  frequency  of  105  cycles  per  sec. 
f  Diameter  of  ALEXANDERSON  generator. 

213 


214 


WIRELESS  TELEGRAPHY 


the  magnetic  reluctance  is  a  minimum,  the  magnetic  flux  passing  through 
the  armature  cores,  EI  and  Ez,  a  maximum.  When,  now,  a  space  in- 
stead of  a  tooth  lies  between  armature  coils,  the  air  gap,  and  hence  the 
magnetic  reluctance,  are  much  larger,  so  that  the  amount  of  flux  through 
the  armature  windings  is  very  small.  Hence  as  the  movable  part,  J, 

rotates,  the  magnetic  jflux  passing 
through  the  armature  coils  varies  peri- 
odically between  a  maximum  and  a 
minimum  value,  so  that  an  oscillatory 
e.m.f.,  whose  frequency  =  the  product 
r.p.m.  X  number  of  teeth,  is  induced 
in  the  armature  winding. 

The  rotor  of  ALEX  ANDERSON'S  ma- 
chine is  shaped  like  the  cross-section, 
J,  in  Fig.  256  and  has  300  teeth.  The 
space  between  the  teeth  is  filled  with 
a  non-magnetic  material  (phosphor- 
bronze)  so  that  the  surface  of  the  rotor, 
J,  is  quite  smooth,  thereby  preventing 
any  material  loss  due  to  air  friction 
(windage). 

The  armature  winding,  in  which  the 
oscillatory  e.m.f.  is  induced,  does  not, 
properly  speaking,  consist  of  coils,  but 
of  a  single  wire  wound  in  a  wave- 

shaped  form  (Fig.  257)  ;  any  two  such  consecutive  U-formed  wires  may  be 
considered  as  a  pair  of  coils  of  one  turn  each,  joined  in  series  but  so  as  to 
oppose  each  other.  Fig.  258  shows  one-half  of  the  completed  armature. 
The  capacity  of  the  machine  —  shown  with  its  D.C.  motor  in  Fig.  259* 
•  —  increases  as  the  air  gap  between  the  armature  and  the  rotor  is  decreased. 
It  was  2.1  kw.  in  one  machine  having  a  0.37  mm.  air 
gap.  The  author  has  no  record  of  its  efficiency. 

b.  A  second  machine  with  a  frequency  of  50,000 
cycles  per  sec.  (\  =  6000  m.)  and  a  capacity  of  35 
kw.  is  shown  in  Fig.  260.     This  alternator  was  also 
designed  by  ALEXANDERSON  and  has  a  diameter  of 
about  1  m.     Further  details  had  not  been  published 
at  the  time  of  writing. 

c.  R.  A.  FESSENDEN196  has  described  still  another 

high  frequency  generator.  Like  ALEXANDERSON'S  machine,  it  is  also  of 
the  inductor  type,  but  is  characterized  in  that  its  movable  portion  (J, 
Fig.  256)  acts  at  the  same  time  as  the  short-circuited  armature  of  an 

*  High  frequency  alternator  to  the  left,  coupling  in  the  middle  and  motor  at  the 
right.    Diameter  of  alternator  about  30  cm. 


FIG.  256. 


s 
v 


FIG.  257. 


HIGH  FREQUENCY  MACHINES  FOR  UNDAMPED  OSCILLATIONS  215 


FIG.  258. 


FIG.  259. 


216 


WIRELESS  TELEGRAPHY 


A.C.  motor  (A.C.  frequency  =  500  cycles  per  sec.).  This  machine 
is  very  simple  in  construction  and  is  claimed  to  have  given  2.5  kw.  at 
JV"  =  1  X  105  cycles  per  sec. 


FIG.  260. 

122.  Goldschmidf  s  High  Frequency  Generator. — R.  GoLDscHMiDT197 
has  attacked  the  problem  of  generating  the  high  frequencies  needed  in 
radio-telegraphy  along  a  different  path. 

a.  The  basis  of  his  method  is  as  follows: 

If  a  coil,  R  (rotor),  revolves  in  the  magnetic  field  of  a  fixed  coil,  S 
(Fig.  261),  through  which  a  direct  current  is  flowing,  then  the  frequency, 
N,  of  the  e.m.f.  induced  in  R  is  equal  to  the  number  of  revolutions  of  R 
per  unit  of  time.  But  if  an  alternating  curient  of  frequency  N1  flows 
through  the  coil  S,  it  can  be  shown198  that  the  e.m.f.  induced  in  R  may  be 
considered  as  made  up  of  one  e.m.f.,  8,  of  the  frequency  N  +  Nf  and 
another,  £>',  of  the  frequency,  N  —  N'. 

What  has  just  been  stated  in  regard  to  the  rotor  with  respect  to  the 
stator,  must  necessarily  also  hold  for  the  stator  with  respect  to  the  rotor; 
for  as  the  induction  depends  only  upon  the  relative  motion  of  the  two 
coils,  the  same  result  would  occur  if  the  rotor  were  held  stationary  and  the 
stator  rotated  in  the  opposite  direction.  Hence  we  may  state:  If  an 
alternating  current  of  frequency  Nf  is  flowing  through  the  rotor  while  the 
latter  makes  N  revolutions  per  second,  its  field  will  induce  an  e.m.f.,  8,  of 
frequency  N  +  N',  and  another,  8',  of  frequency  N  —  N',  in  the  stator. 


HIGH  FREQUENCY  MACHINES  FOR  UNDAMPED  OSCILLATIONS  217 

6.  Now  consider  the  arrangement  of  Fig.  262.  The  storage  battery, 
B,  sends  direct  current  through  the  stator  winding,  S.  Then  an  e.m.f.,  81, 
of  frequency  N,  where  N  =  revolutions  per  second  of  the  rotor,  is  induced 
in  the  rotor.  This  e.m.f.  sends  an  alternating  current,  /i,  of  the  same 
frequency  through  the  short-circuited  rotor  winding.  Then,  according 
to  a,  there  is  in  turn  induced  in  the  stator  an  e.m.f.,  82,  of  frequency 
N  +  N  =  2N  and  another,  8'2,  of  frequency  N  —  N  =  0;  the  latter, 
therefore,  is  not  an  oscillatory  e.m.f. 

The  e.m.f.,  82,  induces  a  current  72  in  the  circuit  comprised  of  stator 
winding,  S,  condenser,  C,  and  the  result  of  this  current  is  that  an  alter- 
nating field,  of  frequency  2N,  is  superimposed  upon  the  constant  magnetic 
field  of  the  direct  current. 

This,  according  to  a,  results  in  an  e.m.f.,  83,  of  frequency  2N  +  N  = 
3N,  and  another,  8'3,  of  frequency  2N  —  N  =  N  in  the  rotor,  the  latter 


FIG.  261.  FIG.  262. 

e.m.f.,  8'3,  adding  itself  to  Si.  The  alternating  current  /3,  due  to  S3  and 
of  frequency  3N  flows  through  the  rotor  winding  and,  according  to  a, 
induces  in  the  stator  winding,  S,  an  e.m.f.,  84  of  frequency  3N  +  N  =  4/V 
and  another,  8%,  of  frequency  3N  —  N  =  27V,  the  latter  having  the  same 
frequency  as  82,  upon  which  it  is  superimposed — and  so  on. 

The  result  of  the  arrangement  of  Fig.  262  must  therefore  be  the  forma- 
tion of  alternating  currents  whose  frequencies  are  2N,  4JV,  QN,  etc.,  in 
the  stator  and  A7",  3N,  5N,  etc.,  in  the  rotor. 

c.  However,  what  is  needed  for  radio-telegraphy,  is  an  oscillation  of  one 
single  frequency  in  the  antenna.  To  obtain  this,  GOLDSCHMIDT — this 
comprises  the  second  essential  feature  of  his  method — makes  use  of  the 
resonance  principle,  by  means  of  which  he  brings  the  amplitude  of  the 
oscillation  desired  for  actual  service  and  of  those  oscillations  which  de- 
termine this  useful  oscillation,  to  such  high  values  that  the  amplitudes  of 
the  other  oscillations  disappear  by  comparison. 


218 


WIRELESS  TELEGRAPHY 


Fig.  263  is  the  diagram  used  by  GOLDSCHMIDT  himself  to  explain  this 
method.  The  circuit  RCBD2C^,  which  is  tuned  to  the  frequency  N,  serves 
to  strengthen  the  current  A;  the  amplitude  of  the  rotor  current  depends 
only  upon  the  ohmic  resistance*  of  this  circuit.  At  most  only  a  very 
small  part  of  the  current,  /i,  flows  through  the  condenser  (76,  for  at  the 

frequency,  TV,  the  inductance  of  the 
winding  Z>2  is  made  equal  to  the 
condensance  (or  capacity  react- 
ance) of  the  condenser  C4:*  hence 
the  impedance  of  the  branch  D^C^ 
becomes  much  lower  than  that  of 
the  branch  containing  CB,  whose 
impedance  is  simply  the  conden- 
sance of  condenser  C$. 

The  stator  current  /2,  of  fre- 
quency 2TV,  attains  a  very  great 
amplitude  due  to  the  fact  that  the 
circuit  SCiDiCz  is  tuned  to  the 
frequency  27V.  Furthermore  this 
263.  current  is  prevented  from  flowing 

into  the  antenna  because  the  in- 
ductance of  the  winding  DI  =  the  condensance  of  C2  at  the  frequency  2N. 
The  resonance  circuit  for  the  rotor  current  73,  whose  frequency  is  3TV,  is 


The  circuit  $C2-antenna-groundt  is  tuned  to  the  frequency,  4N,  of 
the  useful  current,  74.  The  latter  flows  with  any  appreciable  amplitude 
only  through  the  antenna  and  not  through  the  shunt  D^C^,  as  the  impe- 
dance of  this  shunt  is  much  greater,  at  this  frequency  than  the  condens- 
ance of  the  antenna  capacity. 

If  it  were  desired  to  use  the  frequency  3N,  the  antenna  would  have  to 
be  connected  to  the  rotor  in  place  of  the  condenser  Cs,  and  the  condenser 
Cz  and  inductance  DI  could  be  omitted  from  the  stator  circuits,  if  Ci  were 

*  It  is  well  known  that  the  current,  7,  in  a  circuit  consisting  of  capacity,  C,  self- 
induction,  L,  and  resistance,  R,  when  the  impressed  or  induced  potential  is  F0,  is  given 
by 


So  that  if  coL  =  — —>  we  obtain 

coC 


i.e.,  only  the  ohmic  resistance,  R,  determines  I  [see  Art.  676]. 

t  The  antenna-ground  circuit  may,  for  the  purpose  in  view,  be  considered  as  simply 
a  condenser. 


HIGH  FREQUENCY  MACHINES  FOR  UNDAMPED  OSCILLATIONS  219 

properly  dimensioned..  This  would  materially  simplify  the  connections 
but,  of  course,  the  frequency  would  only  be  brought  to  three  times  the 
initial  frequency,  the  latter  being  determined  by  the  number  of  poles  and 
speed  of  the  machine. 

d.  At  the  right  of  Fig.  264  is  shown  a  GOLDSCHMIDT  machine  which  was 
put  into  service  by  the  C.LORENZ  Co.  at  the  EBERSWALDE  station  in  April, 
1910.  The  driving  motor  is  at  the  left  and  in  the  center  is  a  gear  case, 


FIG.  264. 

needed  to  bring  the  comparatively  low  motor  speed  up  to  the  high  speed 
required  by  the  generator.  The  latter,  of  course,  is  of  multipolar  con- 
struction and  gives  12.5  kw.  at  a  frequency  of  3  X  104  cycles  per  sec. 
(X  =  10,000  m.)  with  an  efficiency  of  80  per  cent.,  and  8  to  10  kw.  at 
6  X  104  cycles  per  sec.  (X  =  5000  m.).* 

*  In  regard  to  the  high  frequency  generator  of  COUNT  ARCO  (Telefunkeri)  and  his 
method  of  frequency  transformation,199  see  the  remarks  at  the  end  of  the  book  con- 
cerning developments  in  radio-telegraphy  during  the  last  few  years. 


CHAPTER  IX 

UNDAMPED*   OSCILLATIONS   BY  THE  ARC   METHOD 
1.  THE  VARIOUS  ARRANGEMENTS 

123.  The  Problem  and  Its  Solution  by  V.  Poulsen. — The  requirements 
which  undamped  oscillations  must  meet  in  order  to  be  of  use  for  radio- 
telegraphy  are  as  follows: 

1.  Their  frequency  must  lie  within  the  range  used  in  wireless  telegraphy 
(i.e.,  N  must  be  between  about  106  and  4  X  104  cycles  per  sec.,  corre- 
sponding to  values  of  X  from  300  to  8000  m.). 

2.  Their  energy  must  be  sufficiently  great,  and 

3.  Their  amplitude  and  frequency  must  be  nearly  enough  constant  for 
radio  purposes. 

The  arrangement  by  means  of  which  undamped  oscillations  can  be 
produced  in  a  condenser  circuit  is  that  shown  in  Fig.  244,  in  short  it  is 
the  same  as  that  by  means  of  which  a  quenched  gap  circuit  can  be  ex- 
cited with  direct  current.  Whether  this  arrangement  will  give  undamped 
or  damped  oscillations  depends  upon  the  construction  of  the  condenser 
circuit,  the  nature  of  the  gaseous  gap,  F,  the  dynamo  voltage,  the  re- 
sistance and  self-induction  of  the  supply  circuit  and,  finally,  upon  whether, 
and  if  so  to  what  extent  the  condenser  circuit  is  coupled  to  a  secondary 
circuit. 

a.  ELIHU  THOMSON  and  N.  TESLA,  later  also  R.  A.  FESSENDEN,  made 
early200  use  of  this  arrangement  for  the  purpose  of  continuously  exciting 
the  natural  oscillations  of  a  condenser  circuit  by  means  of  direct  current 
[Art.  115].  It  is  highly  improbable  that  either  THOMSON  or  TESLA  suc- 
ceeded in  actually  obtaining  undamped  oscillations  of  such  frequency 
and  energy  as  come  into  question  for  radio-telegraphy.  THOMSON'S 
spark  gap  (the  arc)  had  solid  metallic  electrodes  in  air  at  atmospheric 
pressure;  with  such  electrodes,  however,  and  potentials  of  not  much  more 
than  1000  volts,  it  is  hardly  possible  to  obtain  undamped  oscillations  at 

*  By  "undamped  oscillations,"  the  author  understands  oscillations  of  which  the 
amplitude  remains  unchanged  from  period  to  period  (in  the  arc  method,  oscillations 
of  type  /  or  77  [Arts.  130  and  131]).  The  designation  "continuous"  oscillations  is 
also  frequently  used.  But  against  the  use  of  this  term  stands  the  existence  of  con- 
tinuous oscillations  whose  amplitude  varies  from  period  to  period  (see  Fig.  290  and 
Art.  109e).  The  name  ''continuous"  is  therefore  not  sufficiently  specific  for  the  case 
in  question. 

220 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD  221 

high  frequency,  of  sufficient  regularity  to  meet  even  the  most  modest 
radio  requirements.  TESLA  made  some  use  of  carbon  electrodes,  which 
are  far  more  apt  to  make  the  production  of  undamped  oscillations  feasi- 
ble; but  even  if  he  obtained  undamped  oscillations,  their  frequency  can- 
not have  been  very  high,  as  even  his  highest  discharge  frequency  gave 
an  audible  tone. 

Then,  somewhat  later,  W.  DuoDELL201  experimented  with  the  ar- 
rangement of  Fig.  244  using  carbon  electrodes  and  undoubtedly  obtained 
undamped  oscillations  in  this  way.  In  fact  he  at  that  time  discussed  the 
essential  condition  for  their  production  and  through  his  experiments  this 
method  of  generating  oscillations  became  quite  popular. 

Soon  after  this  the  action  of  damped  oscillations  as  used  in  radio- 
telegraphy  was  investigated  more  thoroughly  and  the  .advantages  of 
low  damping  in  the  transmitter  became  evident.  From  then  on  un- 
damped oscillations  were  the  sole  aim  of  nearly  all  working  in  this  field. 
But  difficulties  were  encountered  when  it  was  attempted  to  bring  the 
frequency  up  high  enough  for  radio  purposes  with  DUDDELL'S  arrange- 
ment. Hence,  after  a  long  series  of  unsuccessful  attempts  it  was  con- 
cluded that  it  is  impossible  to  obtain  undamped  oscillations  of  frequencies 
above  100,000  cycles  per  sec.,  with  DUDDELL'S  arrangement  using  carbon 
electrodes  for  the  arc.  However,  WERTHEiM-SALOMONSON202  disproved 
this  theory  by  obtaining  oscillations  at  400,000  cycles  per  sec.,  using 
DUDDELL'S  method.  But  the  amount  of  energy  which  could  be  drawn 
from  these  oscillations  was  so  slight,  that  his  results  could  not  yet  be 
considered  a  practical  solution  of  the  problem  of  generating  undamped 
oscillations  for  radio-telegraphic  purposes. 

b.  This  problem  was  first  solved  by  PouLSEN.203  He  soon  showed 
that  the  arrangement  of  Fig.  244  would  give  undamped  oscillations  at 
radio-frequencies  and  sufficient  energy,  if  modified  as  follows: 

1.  The  gap  (or  arc,  F,  Fig.  244)  is  placed  in  hydrogen  or  a  gas  contain- 
ing hydrogen. 

2.  The  positive  electrode  of  the  gap  (or  arc)  is  of  copper,  preferably 
cooled  by  circulating  water,  retaining  carbon  only  for  the  negative  elec- 
trode. 

3.  A  magnetic  field  is  caused  to  act  upon  the  arc  (magnetic  blow-out). 
Furthermore,  in  order  to  improve  the  regularity  of  the  oscillations, 

which  is  of  great  practical  importance,  we  should  add  another  require- 
ment, viz., 

4.  One  of  the  electrodes  (the  carbon)  is  slowly  revolved  about  its  axis. 
The  Poulsen  arrangement   ("Poulsen  generator,"   "Poulsen  arc")   is 

therefore  in  principle  that  shown  in  Fig.  265,  in  which,  however,  the  nec- 
essary auxiliary  apparatus  for  rotating  the  one  electrode  is  omitted. 
The  two  iron  cores  with  direct  current  flowing  through  their  windings 
provide  the  magnetic  blow-out. 


222 


WIRELESS  TELEGRAPHY 


The  requirements  as  given  by  Poulsen  are  not  of  equal  importance. 
A  hydrogen  atmosphere  in  the  arc,  perhaps  in  conjunction  with  the  par- 
ticular materials  chosen  by  him  for  the  electrodes,  suffices  to  secure  the 
high  frequency  needed  for  radio-telegraphy  with  sufficient  regularity  of 
the  oscillations.  The  magnetic  field  is  required  only — and  apparently 
is  even  then  not  absolutely  essential — if  a  very  great  amount  of  energy 
is  wanted  from  the  condenser  circuit. 

c.  The  TELEFUNKEN  Co.204  arrived  at  a  somewhat  different  solution 

of  the  problem  through 
tests  made  at  the  sugges- 
tion of  H.  TH.  SIMON. 
The  Telefunken  "high  fre- 
quency lamp"  is  character- 
ized by  the  following  points 
(Fig  266) : 

1.  As  in  the 


FIG.  265. 


POULSEN 
the     negative 
arc  is  of 


generator, 
electrode  at  the 
carbon,  the  positive,  of  copper,  the  latter  being  water-cooled. 

2.  The  arc  burns  in  a  hollow  in  the  copper  electrode,  hence  in  the  gases 
or  vapors  produced  by  the  arc.* 

3.  A  number  of  such  arcs  are  joined  in  series. 

Fig.  267  illustrates  the  construction  of  one  of  these  lamps;  this  form 
was  used  for  a  time  in  connection  with  wireless  telephony,  but  is  no  longer 
in  use.205 

124.  Commercial  Construction  of 
the  Poulsen  Generators.! — a.  Figs. 
268  (C.  LORENZ  Co.)  and  269206  show 
the  earliest  construction  of  the 
POULSEN  generator  with  transverse 
magnetic  field,  according  to  the  dia- 
gram of  Fig.  265.  The  part  con-' 
taining  the  heavy  cooling  vanes  which 
is  known  as  the  "flame  chamber" 
encloses  the  two  horizontal  electrodes  which  can  be  brought  together 
for  an  instant  at  starting  by  means  of  a  lever  arm  (at  the  upper  right 
of  Fig.  268).  The  large  coils  with  their  iron  cores  furnish  the  horizontal 
magnetic  field  across  the  inside  of  the  flame  chamber,  and  the  small 
motor  serves  to  revolve  the  carbon  electrode. 

b.  A  second,  considerably  different  form  of  construction  used  for  radio- 

*  Similar  to  the  burning  of  flaming  arc-lamps. 

t  The  credit  for  developing  the  construction  of  the  POULSEN  generators  rests 
with  the  former  AMALGAMATED  RADIO-TELEGRAPH  Co.  (in  particular  with  MR.  RAUSCH 
YON  TRAUBENBERG207)  and  the  C.  LORENZ  Co.'s  telephone  and  telegraph  works. 


FIG.  206. 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD  223 


FIG.  268. 


224 


WIRELESS  TELEGRAPHY 


FIG.  269. 

telephony  and  wherever  there  is  no  need  of  great  amounts  of  energy, 
is  shown  diagrammatically  in  Fig.  270.     The  arc  is  vertical,  the  copper 

electrode,  which  is  formed  with  large  vanes 
(R),  is  at  the  top  and  the  carbon  electrode, 
which  is  made  of  a  short  piece  of  homogeneous 
carbon,  is  at  the  bottom.  The  magnetic  field 
is  produced  by  a  single  winding,  S,  having  a 
vertical  core,  Eij  and  the  course  of  the  magnetic 
lines  of  force  is  guided  by  means  of  an  iron  ring, 
EZ,  at  the  end  of  the  copper  electrode.  The 
effect  of  the  magnetic  field  is  to  cause  the  arc 
to  move  slowly  about  in  a  circle. 

An    actual    construction   of   this    form    of 
POULSEN  generator  is  shown  in  Fig.  271. 

The  principal  object  attained  by  the  mag- 
netic field  of  this  second  form  is  that  the  arc  is 
constantly  moving  about  from  point  to  point, 
so  that  rotating  the  electrodes  becomes  super- 
fluous. The  disadvantage  of  this  form,  however,  is  that  this  arrange- 
ment makes  it  impossible  to  secure  the  same  magnetic  field  strengths  or 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD 


225 


to  use  them  to  their  best  advantage,  so  that  it  is  not  possible  to  obtain 

as  high  energy  in  the  oscillations  as  with  the  form  having  a  transverse 

magnetic  field.* 

c.  The   hydrogen  atmosphere   was   formerly   obtained   by   causing   a 

stream  of  hydrogen  gas  to  flow  through  the  case  of  the  POULSEN  generator. 

The  hydrogen  was  either  taken 
1  directly  from  tanks,  as  marketed, 
or  chemically  prepared  in  special 
apparatus  by  the  decomposition  of 
water. 

The  method  lately  in  common 
use  is  much  simpler.  A  small  feed 
cup  similar  to  lubricating  oil  cups 
(see  Figs.  268  and  269)  is  located 
over  the  case  and  is  filled  with 
alcohol  which  continuously  drips 
into  the  flame  chamber  where  it  is 
vaporized. 

125.  Use  of  the  Poulsen  Arc 
for  Measuring  Purposes.115 — For 
measurements,  maximum  regular- 
ity of  the  oscillations,  rather  than 
a  great  amount  of  energy  is  the 


Gas 


fas 


FIG.  271. 


FIG.  272. 


essential, 
does    not 


Therefore   a   transverse    magnetic  field  is   undesirable   as   it 
tend    toward    constant   regularity   [Art.    136c].      Moreover 


*  The  KNOCKROE208  Station,  which  was  operated  with  10-15  kw.  oscillatory 
energy,  had  a  transverse  field  of  10,000  lines  of  force  per  sq.  cm.  The  CuLLERCOATs208 
Station  (5  kw.)  was  equipped  with  a  POULSEN  generator  of  the  second  form.  The 
energy  which  can  be  drawn  from  the  oscillations  is  claimed  to  be  about  19  per  cent, 
of  the  total  energy  supplied  by  the  D.C.  generator.207 
15 


226 


WIRELESS  TELEGRAPHY 


it  is  very  important  that  the  condenser  is  not  of  too  great  capacity 
[Art.  135c]. 

a.  For  some  purposes  the  simple  form  of  lamp  shown  in  Fig.  272 
(F.  KIEBITZ)  suffices:  P  is  a  copper  plate  or  disc  cooled  by  water  on  top 
and  K  is  an  adjustable  carbon  electrode.  Hydrogen  bubbled  through 
acetone  is  recommended  for  the  atmosphere  in  the  arc  chamber. 


FIG.  273. 

6.  The  Physikalisch-technische  Reichsanstalt  has  designed  a  POTJLSEN" 
generator  for  measuring  purposes  which  gives  particularly  constant 
oscillations,  but  very  little  energy. 

"In  this  lamp  the  arc  burns  between  a  cooled  outer  copper  cylinder  of  23  mm. 
inside  diameter  and  30  mm.  high  and  the  surface  of  a  homogeneous  carbon, 
22  mm.  thick.  A  magnetic  field  in  the  direction  of  the  axis  of  the  carbon  and 
whose  strength  is  adjustable,  keeps  the  arc  in  constant  rotation,  thereby  prevent- 
ing the  carbon  from  burning  off  unevenly.  Three  screws  at  the  ends  of  the  carbon 
serve  for  centering  it  with  respect  to  the  copper  tube  and  are  so  arranged  that  this 
adjustment  can  be  conveniently  made  even  while  the  lamp  is  burning.  The 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD  227 

magnetic  field  is  produced  by  a  coil  through  which  the  arc  current  flows.  The 
current  is  furnished  by  a  storage  battery  at  240  volts.  A  suitable  series  resistance 
can  be  conveniently  made  from  Nernst  iron  resistors." 

c.  Pig.  273  shows  a  POULSEN  lamp  of  the  C.  LORENZ  Co.,  designed  espe- 
cially for  measuring  purposes.  It  is  provided  with  an  automatic  regulat- 
ing device  (which  can  be  seen  under  the  lamp  proper  in  Fig.  273)  for  the 
arc  and  is  claimed  to  give  very  constant  oscillations  for  long  periods. 

126.  Circuit  Connections  of  the  Poulsen  Transmitter. — a.  Coupled 
Poulsen  Transmitter. — In  the  first  period  following  the  discovery  of  POUL- 
SEN, the  same  method  of  working  as  in  the  BRATJN  transmitter  was  used, 
probably  universally,  i.e.,  the  POULSEN  generator  was  connected  into  a 
condenser  circuit  and  the  antenna  coupled  thereto. 

To  be  sure,  the  condenser  circuit  of  the  POULSEN  transmitter  was  quite 
different  from  that  used  by  BRAUN.  Of  the  requirements  for  the  POULSEN 
circuit,  viz., 

1.  Lowest  possible  damping,  and 

2.  Comparatively  little  capacity  and  large  self-induction, 

the  latter  is  in  direct  contrast  with  those  of  the  BRAUN  transmitter,  where 
the  capacity  is  chosen  as  great  as  possible  [Art.  106d].  The  first  require- 
ment caused  the  use  of  air  or  oil  condensers,  to  prevent  the  loss  due  to 
dielectric  hysteresis  which  occurs  in  solid  dielectrics.  Moreover,  the  use 
of  air  or  oil  condensers  involves  no  such  difficulties  with  undamped  os- 
cillations as  with  the  BRAUN  transmitter,  as  in  the  former  much  lower  po- 
tentials (at  most  a  thousand,  usually  only  a  few  hundred  volts)  and  much 
less  capacity*  are  used. 

The  coupled  POULSEN  generator  is  still  in  use  for  wireless  telephone 
work  (Chap.  XIV),  in  exceptional  cases  also  for  wireless  telegraphy. 

The  coupling  between  the  primary  circuit  and  antenna  was  inductive 
and  loose  in  the  POULSEN  station  at  KNOCKROE.208  Occasionally,  how- 
ever, very  close  coupling  was  used.  A  medium  degree  of  coupling  is  said 
to  be  undesirable,  as  this  tends  to  make  the  frequency  jump  back  and 
forth  between  two  limiting  values. f 

b.  The  uncoupled  Poulsen  transmitter.  If  antennae  of  relatively 
large  capacity  are  used  and  coils  of  considerable  self-induction  are  in- 
serted in  these,  then  the  ratio  of  supplied  to  useful  (converted)  energy  and 
of  capacity  to  self-induction  are  about  the  same  for  a  POULSEN  generator 

*The  capacity  of  the  POULSEN  station  at  KNOCKROE,208  intended  for  transatlantic 
service  was  only  0.03  mf .,  while  the  BRAUN  transmitter  at  NAUEN  had  0.4  mf .  and  the 
MARCONI  station  at  CLIFDEN  had  1.6  mf.  (air  condensers)  capacity  [Art.  108a]. 

f  It  is  usually  stated  that  first  one,  then  the  other  "of  the  two  coupling  waves'* 
appears.  The  author  is  not  aware,  however,  whether  it  has  ever  been  proven  that 
the  two  oscillations,  which  are  apt  to  occur  alternately  in  the  POULSEN  transmitter, 
are  identical  with  the  two  oscillations  which  occur  simultaneously  in  the  coupled 
transmitter  producing  damped  oscillations. 


228  WIRELESS  TELEGRAPHY 

as  for  a  normal  condenser  circuit.  In  this  case,  therefore,  there  is  nothing 
to  be  gained  by  coupling  the  antenna  to  a  condenser  circuit  and  it  is  cus- 
tomary to  connect  directly  into  the  antenna,  which  results  in  a  particu- 
larly simple  arrangement. 

If  the  antenna  capacity  is  relatively  small  the  arrangement  of  Fig.  205 
[Art.  986] — the  POULSEN  arc  being  placed  between  A  andE — is  of  ten  used. 
This  is  frequently  referred  to  as  the  "fly-wheel  connection/'209 

127.  Devices  for  Producing  Signals. — a.  For  telegraphing  with 
damped  oscillations  a  key  which  alternately  makes  and  breaks  the  circuit 
is  sufficient  [Art.  116].  For  undamped  oscillations  this  is  not  so  simple, 
for  the  following  reasons: 

The  distance  between  the  electrodes  which  is  the  most  favorable  for 
the  production  of  the  oscillations,  is  generally  greater  than  the  gap  length 
which  the  dynamo  voltage  would  jump  across  and  form  an  arc.  Hence 
it  does  not  suffice  to  simply  close  the  supply  circuit  by  a  key  in  order  to 
ignite  the  arc. 

This  could  be  overcome  in  two  different  ways.  Provision  could  be 
made  by  means  of  properly  connected  condensers,  inductances  and  also 
transformers  for  producing  a  higher  potential  sufficient  to  form  the  arc, 
whenever  the  supply  circuit  is  closed.  Or  again,  the  key  could  be  so 
arranged  that  whenever  it  is  closed  the  electrodes  are  brought  into  con- 
tact with  each  other  or  very  close  together. 

Both  methods,  however,  have  a  great  fault.  It  is  comparatively 
difficult  to  keep  the  frequency  and  amplitude  of  undamped  oscillations 
constant.  Hence  it  is  of  the  greatest  importance  to  leave  those  condi- 
tions, which  affect  the  oscillations,  unchanged.  It  is  evident  that  if  the 
supply  circuit  is  continually  opened  and  closed,  it  becomes  practically 
impossible  to  obtain  fixed  conditions  and  oscillations  of  the  requisite 
constancy. 

It  follows  that  in  all  devices  intended  for  sending  telegraphic  signals, 
i.e.,  for  alternately  transmitting  and  suppressing  the  waves,  provision 
must  be  made  for  a  minimum  effect  upon  the  oscillations. 

b.  The  following  are  but  a  few  of  the  many  more  or  less  successful 
arrangements  which  have  been  proposed  for  this  purpose. 

The  arrangement  of  P.  O.  PEDERSEN,210  illustrated  diagrammatically 
in  Fig.  274,  is  intended  for  use  in  the  coupled  POULSEN  generator  and  seems 
formerly  to  have  been  used  in  all  the  POULSEN  stations.  If  the  left  end 
of  the  key,  T,  is  pressed  down,  the  aerial  is  connected  to  the  coil  /S2. 
Upon  releasing  T,  the  condenser  circuit,  SzCLR,  is  completed  and  oscilla- 
tions induced  in  it  by  the  primary  circuit,  7.  The  capacity  self-induction 
and  decrement  of  the  condenser  circuit,  S2CLR,  are  made  the  same  as 
the  corresponding  values  of  the  aerial.  Hence  the  primary  circuit  finds 
exactly  the  same  conditions  in  the  secondary  in  either  position  of  the 
key. 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD 


229 


For  the  case  of  direct  connection  of  the  antenna  to  the  POULSEN 
generator,  the  C.  LORENZ  Co.210  proposes  the  insertion  of  an  iron  resist- 
ance in  series  with  a  condenser  circuit*  in  the  antenna  and  short-circuiting 
both  by  means  of  a  key  when  telegraphing. 

c.  In  PEDERSEN'SISI  apparatus  for  rapid  telegraphing,  a  small  portion 

1 


R 


FIG.  274. 

of  the  inductance  inserted  in  the  antenna  is  usually  short-circuited  so 
that  the  waves  radiated  by  the  antenna  are  somewhat  shorter  than  the 
natural  wave-length  of  the  receiver.  When  signals  are  to  be  trans- 
mitted, this  short  circuit  is  then  opened  and  the  receiver  responds  to  the 
waves. 

128.  The  Multitone  Transmit- 
ter of  C.  Lorenz.211 — Aside  from 
the  direct  application  of  un- 
damped oscillations  to  radio-teleg- 
raphy, W.  BURSTYN  proposed  the 
use  of  the  undamped  oscillations 
of  a  condenser  circuit — the  "tone 

circuit" — of    relatively    low    fre-  FlG   275 

quency,  for  affecting  the  spark  of 
a  quenched  gap  circuit  by  the  particular  period  of  this  tone  circuit,  so 


*  The  condenser  circuit  is  connected  into  the  antenna  like  that  (ALBCA)  shown  in 
Fig.  205.  The  condenser  circuit  causes  an  increase  in  the  wave-length  of  the  oscilla- 
tions, whose  amplitude  is  decreased  because  of  the  energy  consumed  in  the  added 
iron  resistance. 


230 


WIRELESS  TELEGRAPHY 


as  to   produce   a  tone  of  this  period   (or  frequency)   in  the  receiving 
telephone.     (This  is  called  a  tone  transmitter.) 

Fig.  275  is  a  sketch  of  the  connections.  CLTF  is  the  quenched  spark 
gap  circuit.  The  supply  circuit,  LoRQ,  is  fed  by  the  direct-current  gen- 
erator, M.  The  tone  circuit,  CiLi,  consisting  of  a  large  condenser,  Ci, 
and  an  inductance,  LI,  is  connected  in  parallel  to  the  spark  gap,  F.  This 
condenser  circuit  oscillates  (undamped)  and  the  effect  is  about  the  same 
as  if  the  direct  current  supplied  by  the  dynamo  had  an  alternating  cur- 
rent (as  from  an  alternator)  of  the  same  frequency  as  that  of  the  tone 
circuit  superimposed  upon  it. 


FIG.  276. 

The  C.  LORENZ  Co.  has  specialized  in  the  construction  of  this  ar- 
rangement under  the  name  of  "multitone"  transmitter  (Fig.  276).  The 
condenser  C  of  the  diagram  (Fig.  275)  is  the  mica  condenser  seen  at  the 
lower  left-hand  corner  of  Fig.  276,  and  the  spark  is  that  shown  in  Fig.  233 
[Art.  11  Id],  The  coil  LI  is  built  with  an  iron  core  and  can  be  seen 
back  of  the  spark  gap  in  Fig.  276.  The  electric  constants  are  so  chosen 
that  the  discharges  of  the  circuit  ~CLTF  (Fig.  275)  are  of  the  form  dis- 
cussed in  Art.  109e,  i.e.,  we  have  a  case  of  impulse  excitation. 

By  means  of  a  keyboard  (on  the  top  of  the  case  in  Fig.  276)  various 
numbers  of  turns  of  the  winding  LI  (Fig.  275)  can  be  chosen,  so  that  the 
frequency  of  the  tone  circuit  and  hence  the  tone  in  the  receiving  tele- 
phone can  be  very  easily  varied  in  this  way.  This  simple  choice  of  tone 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD 


231 


forms  an  advantage  of  this  method  as  compared  to  tone  production  by 
means  of  an  alternator,  although  the  latter  of  course  offers  a  far  greater 
range  in  the  amount  of  energy  used. 

2.  STUDY  OF  THE  ACTION*  OF  THE  ARC 

129.  Characteristic  of  the  Arc.  —  Under  the  term  characteristic  of 
the  arc  (or  of  some  other  current  carrying  conductor)  we  understand  a 
curve  whose  abscissa  are  proportional  to  the  current  in  the  arc  and  whose 
ordinates  are  proportional  to  the  potential  difference  between  the 
electrodes. 

a.  Experimental    Determination.  —  The    direct-current    characteristic 
(so-called  "static  characteristic")  is  obtained  by  simply  measuring  the 
current  with  an  ammeter,  the 

potential  with  a  voltmeter  and 
then  plotting  the  values  so  ob- 
tained in  curve  form. 

If,  however,  the  current 
varies  with  time  as,  e.g.,  an  alter- 
nating current,  the  characteristic 
may  be  found  by  means  of  the  " 
BRAUN  tube,  used  as  shown  in 
Fig.  277.f  The  curve  over 

which  the  spot  on  the  screen  of  the  BRAUN  tube  moves,  is  the  character- 
istic for  that  particular  variable  current  ("dynamic  characteristic"). 

b.  The  Static  Characteristic  of  the  Arc.107  —  In  Art.  96,  it  was  shown  that 
with  direct  current,  within  certain  limits  the  voltage  across  the  arc,  V,  in 
terms  of  the  current,  /,  is 


where  a  and  b  are  constants.     Hence,  the  characteristic  is  an  equilateral 
hyperbola  (Fig.  278).     It  is  said  to  be  a  "falling"  characteristic,  as  an  in- 
crease in  the  current  corresponds  to  a  decrease  in  the  voltage. 
For   very   large    currents 

V  =  constant  =  a 

*  The  explanation  of  what  takes  place  in  the  arc  method  is  due  primarily  to 
W.  DUDDELL,  A.  BLONDEL,  H.  TH.  SIMON  and  H.  BARKHAUSEN.212  There  seems 
lately  to  have  been  a  widespread  impression  that  the  work  of  these  investigators 
effected  POULSEN'S  invention,  i.e.,  as  if  POULSEN  had  simply  drawn  more  or  less  evi- 
dent conclusions  from  existant  theories.  This,  however,  is  an  anachronism.  POULSEN 
applied  for  his  patents  in  1902  and  1903,  i.e.,  2-3  years  previous  to  any  of  the  theo- 
retical work  which  might  come  into  consideration. 

t  CiC2  are  small  plates  for  the  purpose  of  electrically  deflecting  the  cathode  rays; 
A  is  the  conductor  whose  characteristic  is  being  determined. 


232 


WIRELESS  TELEGRAPHY 


For  very  small  currents,  the  equation  given  above  does  not  hold,  par- 
ticularly when  /  =  0,  V  does  not  become  infinity,  but 

V  =  Vz 

i.e.,  equal  to  the  discharge,  "ignition, "  or  breakdown  potential  which  is  just 
sufficient  to  jump  across  the  gap.  In  Art.  42  it  was  shown  that  this  value 
depends  upon  the  shape  of  the  electrodes  and  the  distance  between  them, 
and  also  upon  the  nature  of  the  gas  in  the  gap.  It  is  far  greater  than  the 
potential  which  exists  across  the  electrodes  of  the  arc,  while  the  latter  is 
burning  with  even  moderate  intensity*  [see  Table  V]. 


FIG.  278. 


FIG.  279. 


c.  The  dynamic  characteristic  for  alternating  current  has  the  shape  of 
the  curve  shown  in  Fig.  279.  The  following  important  points  about  it  are 
noticeable : 

1.  The  value  of  the  potential  corresponding  to  a  given  current  value 
is  not  the  same  when  the  current  is  increasing  as  when  it  is  decreasing. 
Also  there  is  a  phase  displacement  between  the  current  and  the  voltage; 
the  latter  is  not  at  its  maximum  at  the  same  instant  as  the  current,  f 

2.  The  discharge  potential,  Vz,  i.e.,  in  this  case,  the  potential  at  which 

*  If  the  distance  between  the  arc  lamp  carbons  is  ^  mm.,  then  Vz  is  in  general 
more  than  1000  volts,  while  the  potential,  at  the  time  the  arc  is  burning,  is  of  the 
order  of  50  volts. 

f  As  these  relations  are  very  similar  to  those  which  exist  between  magnetic  force 
and  magnetic  field  strength  in  iron,  H.  TH.  SiMON212  has  given  the  phenomenon  the 
name  of  "arc  hysteresis."  These  phenomena  are  closely  related  to  the  fact  that 
the  number  of  ions  existing  between  the  electrodes  depends  upon  the  current  and  the 
temperature  of  the  electrodes  at  the  preceding  instant,  the  number  increasing  as  the 
current  and  electrode  temperature  increase.  Hence  with  rising  current  the  number 
of  ions  is  less  at  a  given  current  value  than  with  decreasing  current  at  the  same  current 
value,  and  the  voltage  necessary  to  produce  a  given  current  is  greater  in  the  first 
case  than  in  the  second  for  the  same  reason. 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD 


233 


the  current  passes  through  zero  is  comparatively  very  low,  as  the  gaseous 
path  remains  ionized  even  after  the  current  has  disappeared.  This  is  due 
to  the  fact  that  in  an  ionized  gas  a  little  time  is  always  required  before  the 
ionization  has  entirely  disappeared  [Art.  65a],  and  also  largely  to  the  fact 
that  the  electrodes,  as  long  as  they  remain  in- 
candescent, emit  electrons  which  tend  to  ionize 
the  gas  [Art.  42c]. 

130.  Type  I  Oscillations. — 7i0  <  70.  Con- 
sider the  arrangement  shown  in  Fig.  280.  The 
resistance,  RQ,  and  the  coefficient  of  self-induc- 
tion, 7/o,  of  the  supply  circuit  are  first  chosen  so 
great  that  neither  the  current  in  the  condenser 
circuit,  CLR,  nor  the  conditions  existing  in  the 
arc  can  have  an  appreciable  effect  upon  the 
supply  current,  IQ,  which  may  therefore  be  con- 
sidered as  constant. 

In  the  case  of  type  I  oscillations,  i.e.,  oscilla- 
tions in  which  the  amplitude,  7i0,  of  the  alternat- 
ing current  is  less  than  the  supply  current  IQ,  the 
current  curve*  is  of  the  form  of  the  heavy  full 
line  curve  shown  in  Fig.  281.  It  follows  that 
we  obtain  an  undamped,  almost  sinusoidal,  alter- 
nating current  in  the  condenser  circuit  with  type  I 
oscillations.  The  voltage  across  the  arc  is  not 
sinusoidal,  but  varies  about  as  shown  by  curve 
V  in  Fig.  289. 

The  characteristic  of  the  arc  with  these  oscillationsf  has  the  form  of  the 
heavy  full  line  curve  of  Fig.  282.  The  values  of  the  supply  current,  7o, 
and  of  the  D.C.  voltage,  VQ,  corresponding  to  it|  are  shown  as  heavy 

dashed  lines  which  divide  the 
plane  of  the  paper  into  four 
quadrants  marked  7,  77,  777, 
IV.  Now,  not  only  for  type  7 
oscillations,  but  in  all  cases 
where  a  direct  and  alternating 
current  are  superimposed  the 
following  condition  holds:  As 


FIG.  280. 


A     A 


W 


FIG.  281. 


long    as    the    characteristic    lies 
within  the  quadrants  II  and  IV, 
energy  is  added  to  the  alternating  current,  while  when  the  characteristic 

*  In  Fig.  281  and  the  following  figures  the  ordinates  to  the  left  represent  values 
of  /i,  those  to  the  right,  of  /  (current  in  the  arc  =  /o  +  /i). 
f  And  with  homogeneous  carbons  and  slow  oscillations. 
}  In  the  static  characteristic. 


234 


WIRELESS  TELEGRAPHY 


lies  in  the  other  two  quadrants,  7  and  ///,  energy  is  taken  from  the 
alternating  current.  The  diagram,  however,  gives  no  indication  of  the 
amount  of  the  energy  changes. 

131.  Type  II  Oscillations. — /io  >  70;  No  Re-ignition.  As  soon  as  the 
amplitude  of  the  alternating  current,  Ji,  becomes  greater  than  the  supply 
current,  Jo,  then  during  the  half  period  in  which  /i,  flowing  through 


FIG.  283. 


the  path  AB  (Fig.  280),  has  the  opposite  sign  (direction)  to  that  of  /0,  the 
current/  =  /i  +  /o  in  AB  must  =  0.  Consequently  the  arc  is  extinguished 
and  does  not  form  again  until  the  voltage,  V,  across  the  electrodes  has 
reached  the  value  of  the  breakdown  potential,  Vz. 

a.  Figs.  283,  284  and  285*  represent  a  series  of  cases  diagrammatically, 
under  the  assumption  that  the  ignition  of  the  arc  takes  place  suddenly 


FIG.  284. 


FIG.  285. 


and  that  the  voltage  across  the  arc  while  burning,  Vb,  remains  constant. 
Fig.  283  represents  the  case  in  which  the  current  amplitude  in  the  con- 
denser circuit,  /!<,,  is  only  slightly  greater  than  the  supply  current  /o;  in 

*  Figs.  283  to  287  and  290  are  drawn  from  figures  of  H.  BARKHAUSEN.212  In 
these  figures  the  full  line  voltage  curve  represents  the  voltage  between  the  condenser 
coatings,  while  the  heavy  dashed  curve  gives  the  arc  voltage. 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD 


235 


Fig.  284  7i0  is  much  greater  than  IQ.  In  both  cases  it  is  assumed  that  the 
damping  of  the  natural  oscillations  of  the  condenser  circuit  is  not  appre- 
ciable (R  is  very  small).  The  effect  of  having  the  natural  oscillations 
more  highly  damped  is  shown  in  Fig.  285,  which  in  all  other  respects  rep- 
resents the  same  conditions  as  Fig.  283. 

In  each  period,  T,  there  are  two  different  portions,  viz.,  the  subperiod, 
Ti,  called  the  "discharging  stage,"  during  which  the  arc  burns  (7  is  not 
zero),  and  the  subperiod,  T2,  the  "charging  stage,"  during  which  the 
condenser  acquires  its  charge,  the  arc  being  extinguished  and  the  current 
/  =  0. 

During  the  first  subperiod,  TI,  the  curve  of  the  current,  /i,  in  the  con- 
denser circuit  is  part  of  a  sine  curve* — i.e.,  we  have  an  ordinary  alter- 
nating current.  During  the  second  portion,  T2,  the  current  is  a  direct 
current  /i  =  —  IQ.  The  voltage,  V,  across  the  condenser  coatings  varies 
correspondingly:  during  7\  it  is  oscillatory,  during  Tz  it  rises  from  the 
value  Fa,  at  which  the  arc  was  extinguished,  to  the  value,  V2)  at  which 
it  is  again  ignited,  rising  approximately  in  a  straight  line.f 

The  voltage,  F,  across  the  arc  falls  abruptly  from  the  value,  Vz,  which 
it  has  at  the  moment  of  ignition,  to  the  value,  F&,  which  it  has  during  the 


t 

\ 

^4- 

^ 

_^ 

*o     J 

ro              70+/]^/ 

V  t 

1 

o     /j, 

I 


FIG.  286. 


FIG.  287. 


time  of  burning  and  then  remains  constant  during  the  entire  time  TI. 
During  the  time,  T%,  in  which  the  arc  is  extinguished,  and  hence  no  cur- 
rent is  flowing  through  the  arc,  the  voltage  V  is  practically  identical 
with  Vc  (voltage  across  condenser  coatings) ;  only  with  relatively  high  re- 
sistance, Ri,  and  the  consequent  high  damping,  does  V  differ  somewhat 
from  Fc. 

b.  The  assumed  conditions  governing  Figs.  283,  284  and  285,  would 
give  an  arc  characteristic  of  the  form  of  Fig.  286.  Actual  experimental 

*  With  decreasing  amplitude,  if  there  is  any  damping. 

f  It  is  assumed  that  70  =  const.  The  actual  form  of  the  charging  curve  depends 
upon  the  capacity  of  the  condenser,  the  resistance,  R0,  and  the  self-induction,  L0 
(the  dynamo  voltage  being  assumed  constant).  If  L0  is  very  great  then  the  charging 
curve  is  almost  a  straight  line,213  while  if  R0  is  very  large  and  L0  is  very  small,  the 
curve  is  a  more  or  less  straight  portion  of  an  exponential  curve.214 


236 


WIRELESS  TELEGRAPHY 


observation,  however,  produces  the  form  shown  in  Fig.  287.  It  follows 
therefore  that  the  assumptions  made  in  a  are  not  quite  correct.  The  ig- 
nition is  not  so  sudden  and  the  voltage  does  not  fall  abruptly  from  Vz  to 
Vb,  nor  does  it  remain  entirely  constant  while  the  arc  is  burning,  but 
rises  slightly  just  before  the  arc  is  extinguished.  Hence  the  variation 


A            A 

/   V                .     /  \ 

/            ^                   .^ 

/ 

-—••—•**  —  - 

—  -1  —        -_>^.  —  1^  —  . 

-f  — 

/ 

/ 

FIG.  288. 


FIG.  289. 


of  voltage  must  be  about  as  represented  by  the  curve  of  Fig.  288.  This 
compares  well  with  the  curve  of  Fig.  289  which  A.  BLONDEL212  determined 
experimentally. 

There  is  another  point  in  which  the  actual  facts  differ  from  the  as- 
sumptions made  in  a,  according  to  which  the  voltage  Vc,  across  the  con- 
denser coatings  could  not  rise  above  the  terminal  voltage  of  the  dynamo. 
As  a  matter  of  fact  it  may  under  certain  conditions  rise  to  a  much  higher 
value. 

That  this  may  be  possible  is  understood  if  we  consider  that  a  change 

in  Jo — the  previous  assumption  that 
/o  is  constant  is  not  entirely  correct — 
may  produce  higher  potentials  be- 
cause of  the  self-induction,  Z/o,  by 
adding  to  the  voltage  across  the  con- 
denser terminals  [see  Art.  1156]. 
Whether  this  is  always  the  sole  ex- 
planation is  a  question  which  need 
not  be  further  investigated  here. 

132.  Type  III  Oscillations  /i0  > 
70;  Re-ignition  Present.— Fig.  285 
shows  that  at  the  moment  the  arc  is 
extinguished,  the  voltage  across  the 
electrodes  jumps  from  the  normal 
value  Vb  to  the  value  Va.  Va  is  not  as  high  as  the  ignition  voltage  Vz, 
which  is  just  sufficient  to  start  the  arc  at  the  end  of  the  charging  stage, 
T2.  Under  certain  conditions  in  fact,  the  gas  between  the  electrodes 
may  still  be  so  largely  ionized  immediately  after  the  arc  is  extinguished, 
that  a  much  lower  voltage,  e.g.,  Va,  suffices  to  at  once  re-ignite  the  arc 
("re-ignition"). 


FIG.  290. 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD 


237 


If  this  is  the  case,  then  the  oscillatory  discharge  of  the  condenser  con- 
tinues, until  finally  the  voltage  Va  becomes  too  low  to  maintain  the  arc 
which  is  then  extinguished.  Hence,  we  obtain  oscillations  of  the  form  of 
Fig.  290  or  291.  The  latter  form  is  practically  a  representation  of  a  rapid 
sequence  of  the  natural  oscillations  of  the  condenser  circuit.  It  is  noth- 
ing more  nor  less  than  the  form  of  oscillation  whose  practical  application 
was  discussed  in  Chap.  VII.* 


FIG.  291. 


133.  Energy  of  the  Oscillations. — a.  Type  I  Oscillations. — Experience 
has  shown  that  these  cannot  be  produced  so  as  to  give  great  energy  by  such 
means  as  are  known,  the  difficulty  of  obtaining  high  power  increasing  as 
the  frequency  becomes  higher. 

b.  Type  II  Oscillations. — Under  the  same  assumptions  upon  which 
Fig.  285  was  based  (7o  =  const.,  V  =  const,  and  during  time  arc  is  burn- 
ing V  =  Vb)}  the  energy  which  is  supplied  to  the  oscillation  during  one 
period  by  the  direct  current,  and  hence  the  maximum  which  can  possibly 
be  drawn  from  the  oscillation,  is  approximately 


R 

2L 


Ti 


-  e 


where  C,  R  and  L  are  the  capacity,  resistance  and  coefficient  of  self-in- 
duction of  the  condenser  circuit.  Hence  with  R  and  L  and  also  Vb  con- 
stant, the  energy  increases  very  rapidly  with  increasing  ignition  voltage. 
c.  Type  III  Oscillations. — In  the  pure  form  of  these  oscillations  (Fig. 
291)  we  deal  practically  with  the  natural  oscillations  of  the  condenser 

*  The  natural  oscillations  of  a  condenser  circuit  discussed  in  Chap.  I  are  also 
practically  the  same  as  those  described  here.  The  difference  is  merely  that  in  the 
case  mentioned  in  Chap.  I,  the  supply  current  is  not  constant  or  even  nearly  so, 
but  varies  widely  with  the  time,  being  furnished  from  either  an  induction  coil  or  an 
A.C.  transformer. 


238  WIRELESS  TELEGRAPHY 

circuit.     The  energy  which  is  transferred  in  one  discharge,  is  approxi- 
mately  [Art.   66]. 


at  the  same  time  the  highest  voltage,  Vz,  which  occurs  across  the  con- 
denser, may,  under  certain  circumstances,  be  greater  than  the  dynamo 
voltage  (see  Art.  1316).  The  energy  consumed  per  second  by  the  oscilla- 
tions is 

r  .  \  cvs 

where  £  is  the  discharge  frequency.  This  depends  upon  the  rapidity  with 
which  the  condenser  becomes  fully  charged  again  after  discharging;  for  a 
given  capacity,  it  increases  as  the  supply  current,  /o  is  increased. 

134.  Frequency  of  the  Oscillations.215  —  a.  The  frequency  of  type  I 
oscillations  is  determined  partly  by  the  self-induction  and  capacity  of  the 
condenser  circuit,  partly  by  the  characteristic  of  the  arc.  The  frequency 
is  always  somewhat  lower  than  the  theoretical  value  of  the  natural  fre- 
quency of  the  condenser  circuit  as  obtained  by  THOMSON'S  equation  from 
the  known  values  of  the  coefficient  of  self-induction  and  the  capacity,  but 
the  difference  is  never  very  large. 

6.  In  type  II  oscillations  the  period  T  consists  of  two  parts,  T\  and 
T2.  The  length  of  the  discharging  period,  TI,  is  determined  first  of  all  by 
the  period  of  the  natural  oscillations  of  the  condenser  circuit  and  the  ratio 
7i0:/o;  secondly,  by  the  damping  of  the  natural  oscillations  (see  Figs. 
283  and  285).  The  second  or  charging  period,  T^,  is  the  interval  from 
the  time  the  arc  is  extinguished  to  the  time  it  is  again  ignited.  The  period 
of  the  oscillation,  T  =  TI  +  T2,  can  therefore  not  be  found  even  approxi- 
mately by  means  of  THOMSON'S  equation,  as  it  depends  materially  upon 
the  rapidity  with  which  the  condenser  becomes  charged,  i.e.,  upon  condi- 
tions in  the  supply  circuit. 

A  consideration  of  practical  importance  is  that  not  only  the  amplitude 
but  also  the  length  of  the  period  and  hence  the  frequency  varies  if  there  is 
any  slight  change  in  the  voltage  at  which  the  arc  ignites.  This  is  what  gen- 
erally happens  as  soon  as  there  is  the  least  change  in  the  electrodes.  The 
extent  of  the  change  in  772  depends  largely  upon  the  manner  in  which 
the  voltage  rises  to  the  ignition  point  after  the  arc  has  been  extinguished 
and  upon  the  manner  in  which  the  voltage,  V,  across  the  electrodes  rises.  * 

c.  For  the  pure  type  III  oscillations^  (Fig.  291),  practically  the  same 

*  At  the  points  where  the  V  curve  (Fig.  283  et  seq.)  cuts  the  "ignition  character- 
istic" (abscissae  «  time,  ordinates  a  Vz)  the  V  curve  must  be  much  steeper  than  the 
ignition  characteristic  so  that  ignition  always  takes  place  promptly.  The  ignition 
characteristic  becomes  steeper,  the  more  rapidly  the  ionization  of  the  gas  disappears. 

f  Type  II  oscillations  of  the  kind  shown  in  Fig.  290  are  in  general  entirely  irregular 
and  quite  useless. 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD  239 

may  be  stated  as  for  the  natural  oscillations  of  condenser  circuits  pro- 
duced by  an  induction  coil  or  similar  device  [Chap.  I].  The  effect  of  the 
arc  on  the  period*  is  not  appreciable,  the  frequency,  therefore,  is  constant 
and  determined  by  the  self-induction  and  capacity  from  THOMSON'S 
equation;  as  long  as  the  distance  between  the  electrodes  is  at  least  2  mm. 
If  this  distance  is  very  small,  so  that  the  deionization  becomes  very  rapid, 
then  in  this  case  also,  the  frequency  may  be  considerably  lower  than  would 
be  expected  from  THOMSON'S  equation  [Art.  5c]. 

135.  Practical  Conclusions!  for  Type  II  Oscillations. — Type  /  oscil- 
lations, because  of  their  low  energy  are  of  no  practical  importance. 
Only  Type  II  oscillations  are  used  for  radio-telegraphy  with  undamped 
oscillations. 

In  practice  it  is  important  to  give  the  oscillations  as  much  energy  as 
possible  %  and  to  keep  the  frequency  as  nearly  constant  as  possible. 

a.  The  requirement  of  maximum  energy  leads  to  the  maximum  igni- 
tion voltage  [Art.  1336].     This  can  be  provided  for  in  two  ways,  viz., 

1.  By  lengthening  the  charging  stage,  T2,  as  much  as  possible,  so  as  to 
give  the  gas  plenty  of  time  to  deionize. 

2.  By  the  use  of  special  means  for  rapid  deionization  of  the  gas. 

The  first  method  involves  the  danger  of  destroying  the  constancy  of  the 
frequency  [Art.  136c].  Moreover,  the  longer  T2  is  made,  the  more  does 
the  current  curve  tend  to  differ  from  the  sinusoidal  form  (see  Fig.  284), 
i.e.,  the  upper  partial  oscillations  come  into  prominence  in  addition  to  the 
fundamental.  The  energy  of  the  partial  oscillations  is  wasted,  however, 
for  in  practice,  when  coupling  or  when  using  a  tuned  receiver,  only  the 
fundamental  oscillation  is  effective. 

As  a  matter  of  fact,  therefore,  it  is  best  to  work  with  oscillations  in 
which  the  subperiod,  T2,  is  relatively  short,  and  in  which,  therefore,  /lo  is 
not  much  different  from  7o  (Fig.  285). 

b.  Then,  however,  it  is  especially  important  to  obtain  a  very  rapid 
'growth  of  the  ignition  voltage  by  special  means,  i.e.,  to  deionize  the  gas  in  the 

path  of  the  arc  as  rapidly  as  possible.  Necessary  precautions  for  this 
result  are  as  follows: 

1.  Removal  of  the  ionized  gas  from  the  space  between  the  electrodes. 

The  spontaneous  deionization  of  the  gas  in  the  path  of  the  arc,  due  to 
the  ions  recombining,  is  in  general  too  slow  to  be  effective  at  the  high 

*  That  is,  the  period  of  the  damped  oscillations  (T  in  Fig.  291)  which  come  into 
consideration  for  practical  use. 

f  Strictly  speaking,  conclusions  may  be  drawn  from  what  has  preceded  only  if 
the  condenser  circuit  is  not  coupled  to  some  other  circuit.  If  it  is  loosely  coupled 
to  another  circuit,  the  conditions  will  presumably  change  but  very  little,  but  with 
close  coupling  they  will  change  very  much.  Systematic  investigation  of  the  coupling 
of  Type  //  oscillations  has  to  date  been  made  only  at  low  frequencies  (S.  SuBKis970). 

J  The  important  thing,  of  course,  is  to  take  as  much  energy  as  possible  from  the 
oscillations. 


240  WIRELESS  TELEGRAPHY 

frequencies  involved.  Moreover,  as  the  electrodes  are  not  so  very  close 
together  as  with  quenched  spark  gaps,  deionization  by  absorption  at 
the  electrodes  and  by  an  electric  field  cannot  amount  to  much.  Diffusion 
into  the  outer  space  is  far  more  effective,  particularly  if  the  coefficient  of 
diffusion  of  the  gas  in  question  is  high;  hence  hydrogen,  having  the 
highest  coefficient  of  diffusion,  gives  the  best  results.  The  most  effective 
means  of  removing  the  ions  in  the  space  between  the  electrodes  is  the 
use  of  a  magnetic  blowout,  as  this  acts  while  the  current  is  still  flowing, 
driving  the  arc  and  the  gas  contained  in  the  arc  out  of  the  innermost 
recesses  between  the  electrodes.111 

The  use  of  a  mechanical  air  blower  for  this  purpose  hardly  offers  any 
advantages.  To  be  effective  the  velocity  of  the  current  of  air  or  gas  blown 
must  be  such  that  each  particle  of  the  air  moves  through  a  distance  of  at 
least  1-2  mm.  during  the  half  period  of  an  oscillation  (at  X  =  1000  m.,  this 
would  be  1.5  X  10~6  sec.).  Such  high  velocities,  however  (600  to  1200 
m.  per  sec.  under  the  assumptions  made),  aside  from  the  complications  in- 
volved, would  produce  such  eddies  between  the  electrodes  as  to  defeat  the 
very  object  in  view  and  make  a  complete  removal  of  the  ions  in  the  path 
of  the  arc  impossible,  in  spite  of  the  high  velocity. 

2.  Prevention  of  the  ionizing  effect  of  the  incandescent  electrodes, 
particularly  of  the  anode.  The  following  are  various  methods  for  pre- 
venting or  at  least  reducing  this  effect. 

a.  Cooling  the  anode,  at  which  the  development  of  heat  is  particularly 
great. 

Cooling  the  anode  as  a  whole  is  relatively  a  simple  matter.  Water  or 
air  cooling,  the  latter  preferably  aided  by  ventilators  or  a  ribbed  con- 
struction of  the  anode,  suffice.  But  it  is  much  more  difficult  to  prevent 
local  heating  at  the  point  where  the  arc  originates  and  at  which  the  emis- 
sion of  electrons  continues  after  the  charging  stage.  This  detrimental 
effect  can  be  mitigated  by: 

a.  Use  of  a  metal  having  very  high  heat  conductivity  (as  copper  or  sil- 
ver) for  the  anode.* 

/?.  Surrounding  the  electrodes  by  a  gas  having  very  high  heat  con- 
ductivity; in  this  respect,  hydrogen,  which  has  the  greatest  heat  conduc- 
tivity of  all  the  gases,  is  best. 

7.  Hydrogen,  moreover,  has  the  advantage  of  preventing  the  forma- 
tion of  metallic  oxides  and  even  reducing  any  previously  existing  oxides, 
which  are  particularly  active  in  the  emission  of  electrons  when  incandes- 
cent. This  is  also  true  to  a  certain  extent  of  an  enclosed  arc-lamp. 

b.  Rotating  one  or  both  of  the  electrodes  tends  to  reduce  local  heating 
only  if  it  is  so  rapid  that  the  base  of  the  arc  is  moved  sufficiently  far  in 
each  period  as  to  occur  at  a  point  not  yet  materially  heated  in  the  succeed- 

*  Homogeneous  carbon  is  used  universally  for  the  cathode.  This  difference  or 
asymmetry  of  the  two  electrodes  is  also  of  value  in  that  it  prevents  re-ignition. 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD  241 

ing  period.  This,  however,  would  require  a  speed  of  rotation  of  a  much 
higher  order  than  is  ever  used. 

c.  The  subdivision  of  the  arc  into  several  partial  arcs  [Art.  123c]  in 
series  is  often  advantageous.  With  the  same  total  voltage  and  the  same 
current,  about  the  same  amount  of  heat  is  developed  in  all  the  partial  arcs 
as  in  the  equivalent  single  arc,  but  the  heat  given  off  is  much  greater  in  the 
combined  partial  arcs  than  in  the  single  arc. 

The  problem  of  deionizing  the  gaseous  path  of  the  arc  during  the  charg- 
ing stage  and  keeping  it  deionized  increases  in  difficulty,  other  things 
being  equal,  as  the  frequency  of  the  oscillation  is  increased,  the  time  avail- 
able for  the  deionization  being  correspondingly  shortened,  and  as  the  cur- 
rent and  hence  also  the  heating  of  the  electrodes  and  the  number  of  ions 
formed  are  increased.  Therein  lies  the  main  explanation  of  the  relative 
ease  with  which  undamped  oscillations  of  low  frequency  and  energy  can  be 
obtained,  while  for  a  long  time  no  one  succeeded  in  obtaining  undamped 
oscillations  of  such  frequency  and  energy  as  are  needed  in  radio-telegraphy . 

c.  Amount  of  Capacity  Allowable. — Let  the  dynamo  voltage  and  the 
frequency  of  the  oscillations  be  given.  Then  the  energy  supplied  to 
the  condenser  circuit  per  second  is  proportional  to  the  capacity  in  this 
circuit  [Art.  1176].  Hence,  from  this  standpoint,  a  larger  capacity  is 
advantageous.  On  the  other  hand  a  larger  capacity  necessitates  a  larger 
current  amplitude,  7i0,  in  the  condenser  circuit,  and  as  this  must  not  be 
much  larger  than  the  supply  current,  70  [see  a],  the  latter  must  also 
be  larger.  But  the  greater  the  current  through  the  arc  becomes,  the 
more  intense  will  be  the  heating  of  the  electrodes  and  the  ionization  of 
the  gas  in  the  path  of  the  arc  and  the  less  effective,  therefore,  will  be 
the  curative  methods  given  in  b. 

Consequently,  indefinitely  increasing  the  capacity  soon  becomes  detri- 
mental to  the  best  results,  so  that  in  generating  undamped  oscillations 
by  the  arc  method  we  are  obliged  to  work  with  relatively  small  capacity 
and  large  self-induction  in  the  primary  circuit. 

136.  Regularity  of  Type  II  Oscillations  (K.  VoLLMER115). — It  is  evi- 
dently extremely  probable  that  the  burning  of  the  arc  causes  the  electrodes 
gradually  to  change,  much  more  so,  in  fact,  than  in  an  oscillating  damped 
condenser  circuit  of  low  discharge  frequency,  in  which  the  gap  is  without 
current  the  greater  part  of  the  time.  Every  change  in  the  path  of  the  arc, 
however,  will  alter  the  ignition  voltage  and  thereby  the  frequency  and 
wave-length,  as  well  as  the  energy  and  amplitude  of  the  oscillations. 

a.  These  fluctuations  may  be  subdivided  into  the  following  classes : 

1.  Slight  fluctuations  in  arcs  without  transverse  magnetic  field,  these 
being  either 

a.  Rapid  fluctuations,  or 
(3.  Slow   changes. 

16 


242  WIRELESS  TELEGRAPHY 

2.  Great  fluctuations  in  arcs  having  transverse  magnetic  field  and 
caused  by  this  field. 

The  cause  for  1  in  arcs  with  no  transverse  magnetic  field  is  no  doubt  the 
following :  The  arc,  while  burning,  eats  its  way  into  the  electrode  (or 
electrodes)  thereby  gradually  lengthening  the  arc  and  increasing  the  igni- 
tion voltage,  so  that  the  frequency  and  amplitude  of  the  oscillations  are 
also  gradually  changed  thereby.  This  continues  until  the  arc  finds  more 
favorable  conditions  at  some  neighboring  point,  to  which  it  then  jumps 
with  the  result  that  the  arc  length,  ignition  voltage,  frequency  and  am- 
plitude also  take  a  jump  in  the  opposite  direction.  (The  individual  de- 


FJG.  292. 

pressions  or  cavities  which  the  arc  had  eaten  out,  on  its  way  around  the 
hollow  cylindrical  electrode  are  easily  recognizable  in  the  accompanying 
photograph,  Fig.  292.) 

Tests  have  shown  that  changes  in  the  wave-length  and  in  the  ampli- 
tude occur  in  conjunction  with  changes  in  the  average  arc  potential,  in 
fact  the  wave-length  variation  is  directly  proportional  to  the  mean  arc 
potential  variation.  Other  things  being  equal,  it  (the  mean  arc  potential 
variation)  increases  with  increasing  capacity,  decreasing  supply  current 
and  decreasing  wave-length  (increasing  frequency). 

The  extent  of  the  fluctuations  depends  very  largely  upon  the  construc- 
tion of  the  lamp.115  In  a  lamp  made  by  VOLLMEU  and  copied  from  that  of 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD 


243 


the  Physikalische  Reichsanstalt,  he  found  that  when  the  adjustment 
was  particularly  good,  at  X  =  2000  m.  the  intensity  variation  was  about 
2  per  cent.,  the  frequency  variation  about  0.03  per  cent.,  and  at  X  =  700m. 
the  frequency  variation  was  about  0.18  per  cent. 

b.  The  results  of  these  fluctuations  are  disturbances  which  interfere 
with  the  practical  application  of  the  oscillations  as  well  as  with  any 
measurements. 

The  rapid  intensity  fluctuations  which  occur  in  lamps  without  a  trans- 
verse field  are  harmless,  as  the  measuring  instruments  or  detectors  used 
do  not  respond  to  them,  but  indicate  the  average  value.  The  slow  fluc- 
tuations, however,  may  at  times  be  very  annoying  especially  in  connection 
with  measurements. 


FIG.  293. 


The  frequency  fluctuations  interfere  particularly  if  the  arc  circuit  is 
very  loosely  coupled  to  a  secondary  circuit,  (1)  by  flattening  the  reso- 
nance curve,  reducing  the  sharpness  of  resonance  and,  (2)  by  materially 
reducing  the  current  effect  at  resonance. 

1.  In  Fig.  293  the  broken  line  curve  is  the  resonance  curve  which  ought 
to  be  obtained  by  the  action  of  an  undamped  oscillation  of  constant  fre- 
quency upon  a  secondary  circuit  whose  decrement,  di  =  0.005.  The  full- 
line  curve  is  the  resonance  curve  obtained  with  the  same  secondary  circuit, 
if  the  frequency  (or  wave-length)  of  the  undamped  primary  circuit  fluctu- 
ates back  and  forth  at  a  uniform  rate  between  the  limits  X  +  X'  and  X  —  X', 
X7  being  only  0.05  per  cent,  of  X.  It  will  be  noted  that  even  with  this 
small  fluctuation  the  resonance  curve  suffers  a  considerable  flattening  and 
reduction  in  height  from  its  ideal  form. 

The  resonance  curves  obtained  from  arcs  with  a  transverse  field  are  of 
the  form  of  the  full-line  curve  shown  in  Fig.  294  (d2  =  0.012) ;  here  the 
difference  from  the  dashed  curve,  which  would  be  obtained  with  constant 
frequency  using  the  same  secondary  circuit,  is  much  greater.  (The  peaks 
of  the  two  curves  were  drawn  alike  in  height  intentionally.)  From  the 


244  WIRELESS  TELEGRAPHY 

shape  of  the  curve  it  is  evident  that  the  fluctuations  which  occur  are  not 
symmetrical  with  respect  to  a  mean  value,  but  (similarly  to  the  brush 
discharge  of  condensers  [Art.  86])  the  frequency  lies  mainly  near  a  certain 
value  (corresponding  to  €2  =  1450)  from  which  it  gradually  fluctuates 
to  a  lower  value  (corresponding  to  C2  =  1480). 

2.  The  changes  in  the  current  effect  caused  by  the  frequency  fluctua- 
tions, may  be  quite  considerable,  as  is  shown  by  the  following  tabulation 
which  is  based  on  the  assumption  that  the  fluctuations  are  symmetrical, 
amounting  to  0.03  per  cent,  on  each  side  of  the  mean  value  to  which  the 
secondary  circuit  is  tuned. 

d2  X  =  2000  X  =  1000  X  =  500  m. 

0.01  3  per  cent.  24  per  cent.  63  per  cent. 

0.03  0.5  per  cent.  4  per  cent.  16  per  cent. 

0 . 05  0.2  per  cent.  1 . 5  per  cent.  6 . 5  per  cent. 

Qualitatively,  therefore,  the  effect  of  the  frequency  fluctuations  is  the  same 
as  if  the  primary  circuit  had  constant  frequency  but  material  damping. 

c.  In  Art.  125  it  was  already  pointed  out  that  a  transverse  magnetic 
field,  which  is  very  advantageous  for  the  energy  of  the  oscillations,  is  very 
disadvantageous  for  their  regularity.  *  This  is  true  not  only  of  the  trans- 
verse field,  but  more  or  less  so  of  all  agents  which  tend  to  increase  the 
energy.  The  explanation  of  this  fact  is  simple  enough.  The  require- 
ment for  maximum  energy  is  the  most  complete  deionization  of  the  gase- 
ous path  of  the  arc  during  the  charging  stage,  while  on  the  other  hand  a 
slight  ionization  or  electrification  of  the  gaseous  gap  is  advantageous,  in 
fact  is  essential  with  low  potentials  [see  Arts.  426  and  78c]  for  a  sure  and 
accurate  timing  of  the  discharge.  Hence  we  must  fall  back  upon  a  com- 
promise. This  explains  in  part  the  use  of  carbon  as  the  negative  electrode, 
in  spite  of  the  fact  that  its  low  heat  conductivity  lowers  the  ignition  volt- 
age. This  also  explains  why  the  strength  of  the  transverse  magnetic 
field  is  in  general  not  made  very  great,  sacrificing  a  further  increase  in  the 
energy  of  the  oscillations. 

Somewhat  of  an  exception  to  this  rule  is  encountered  in  the  use  of 
hydrogen,  one  of  whose  properties  tends  greatly  to  increase  the  regularity 
of  the  oscillations;  namely,  the  relatively  low  breakdown  potential  of 
hydrogen  corresponding  to  a  given  gap  length  [Art  42c].  The  consequence 
thereof  is  that  with  a  given  voltage  (ignition  voltage)  the  distance  between 
the  electrodes  can  be  made  considerably  greater  when  hydrogen  is  used 
than,  for  example,  with  air.  Hence  any  change  in  the  arc  length  (say  due 
to  eating  away  or  volatilization  of  the  electrodes)  amounts  to  a  lower  per- 

*  The  extent  of  the  fluctuations  depends  upon  the  construction  of  the  lamp  in 
this  case  also.  Good  regularity  can  be  obtained  with  lamps  having  a  transverse 
magnetic  field  (see  Art.  1916),  but  this  is  a  much  more  difficult  attainment  than  with 
lamps  having  no  transverse  field. 


UNDAMPED  OSCILLATIONS  BY  THE  ARC  METHOD  245 

centage  of  the  initial  length  with  hydrogen  than  with  air,  so  that  the  re- 
sultant change  in  the  potential  and  hence  also  in  the  wave-length  and  in- 
tensity is  less  than  with  air. 

137.  The  Terms  "Spark"  and  "Arc."217— Doubt  has  occasionally 
been  expressed  of  late  as  to  whether  the  phenomenon  in  the  gap  consti- 
tuted a  " spark"  or  an  "arc"  in  a  given  case. 

In  the  two  limiting  cases  there  is  never  any  doubt.  Everybody  speaks 
of  " sparks"  when,  as  in  the  early  construction  of  the  BRAUN  transmitter, 
only  a  few,  say  ten  to  twenty  discharges  per  second  occur.  Here  the  periods 
during  which  current  flows  through  the  gap  are  separated  by  long  in- 
tervals of  currentlessness,  so  to  say,  and  the  total  time  during  which  there 
is  no  current  in  the  gap  is  much  greater  than  the  total  time  during  which 
current  flows  through  the  gap.  Here,  then,  both  eye  and  ear  receive  evi- 
dence of  intermittent  discharges  (limiting  case  7). 

Again,  everybody  would  call  the  phenomenon  obtained  in  the  gap 
between  the  electrodes,  with  undamped  oscillations  of  type  /  or  II,  an 
"arc."  In  type  /  the  gap  is  never  without  current, in  type //  the  periods 
with  and  without  current  alternate  so  rapidly  that  neither  human  sight 
nor  hearing  can  distinguish  between  them  (limiting  case  //). 

Between  these  two  limiting  cases,  however,  are  various  intermediate 
forms,  e.g.,  the  case  of  damped  oscillations  at  a  very  high  discharge 
frequency.  Here  the  total  time  of  currentlessness  becomes  about  equal 
to  or  even  less  than  the  time  of  current  in  the  gap;  at  any  rate  the  eye  can 
here  no  longer  distinguish  the  individual  discharges  and  the  ear  at  best 
can  discover  the  presence  of  intermittent  discharges  only  in  the  tone  or 
note  emitted  by  the  gap.*  Whether,  in  this  case,  we  speak  of  sparks  on 
the  basis  that  the  form  of  the  discharges  is  inherently  the  same  as  in  lim- 
iting case  /,  or  whether  we  speak  of  an  arc,  in  view  of  the  fact  that  in  lim- 
iting case  II,  the  duration  of  current  is  of  the  same  order  as  the  duration 
of  currentlessness,  is  a  matter  of  individual  preference.  At  any  rate,  it 
is  advisable  in  such  a  case  to  obtain  by  actual  test  (e.g.,  by  means  of  a 
discharge  analyzer  or  a  BRAUN  tube)  an  exact  picture  of  the  time  varia- 
tion of  the  discharges,  rather  than  to  dispute  the  propriety  of  the  name 
given  to  the  phenomenon  in  question. 

*  In  scientific  and  patent  literature  it  is  often  claimed  for  some  particular  device 
or  arrangement  that  it  will  generate  undamped  oscillations.  If  such  a  claim  is  based 
solely  upon  the  arc-like  appearance  or  sound  in  the  gap,  it  must  not  be  accepted  with- 
out further  conclusive  evidence. 


CHAPTER  X 
PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE 

1.  OVER  PLANE  OR  SPHERICAL  HOMOGENEOUS  GROUND218 

138.  Ground  Having  Plane  Surface  and  High  Conductivity.* — Of 
these  two  assumptions,  the  latter  is  approximated  in  sea  water.  Under 
both  assumptions  we  would  have  the  following  conditions. 


mi  i  i  I'liiiri 
MIII  |  i  mm 
\\\\\  \  \\\\\\\  \  ! 
\\\VM\\\\\\V;  \\\\\\\   V\\ 

•A\\        \  \\X\\X        \\\\\\  *•'  \  \ 
gx\       \\\\\\>       *"vvX 


FIG.  295. 

a.  General  Nature  of  the  Field. — With  a  transmitter  placed  above  the 
earth's  surface,  the  following  rule  gives  approximatelyf  the  form  of  the 
waves.  Consider  the  ground  removed  and  replaced  by  the  image  of  the 
antenna,  with  respect  to  the  earth's  surface,  so  that  the  antenna  and  its 
image  form  two  symmetrical  halves.  It  is  also  assumed  that  the  distri- 

*  That  is  the  specific  conductivity  >  10~12  c.g.s.  units. 

f  The  results  would  be  absolutely  exact  if  the  conductivity  of  the  earth's  surface 
were  infinitely  great. 

246 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE   247 

bution  of  current  and  potential  is  the  same  as  exists  in  the  symmetrical 
halves  of  the  antennae  shown  in  Figs.  23,  42,  45  et  seq.,  i.e.,  at  any  point,  P, 
and  its  image,  P',  the  current  must  have  the  same  direction  but  the  po- 
tential is  of  opposite  sign  in  each.  The  rule  then  is :  The  waves  which  the 
antenna  with  its  image  would  radiate,  if  they  were  placed  in  free  space, 
have  the  same  course  through  the  air  as  the  waves  which  are  actually  radi- 
ated by  the  antenna  placed  above  the  earth's  surface.219 

b.  Effect  of  the  Form  of  the  Antenna. — From  the  preceding  it  follows 
that  for  a  simple  antenna  (single  straight  wire),  the  electric  field  would  be 


FIG.  296. 

as  shown  by  the  upper  halves  of  Figs.  295  and  296  [see  Art.  20a],  the  former 
representing  the  instant  of  maximum  charge,  the  latter,  the  instant  of 
maximum  current.  As  the  distance  from  the  antenna  increases,  the  electric 
lines  of  force  approach  more  and  more  the  form  of  circular  arcs.  In 
Art.  20a  it  was  stated  that  the  magnetic  lines  of  force  are  also  circular. 

With  other  forms  of  antenna  the  shape  of  the  wave  in  the  vicinity  of  the 
antenna,  up  to  distances  of  one  or  two  wave-lengths,  may  be  considerably 
different  from  that  just  described,  though  the  general  character  of  the 
field,  particularly  the  snapping  apart  of  the  lines  of  force  must  be  more  or 
less  the  same  in  all  forms  of  antennas.220  The  greater  the  distance  from 


248  WIRELESS  TELEGRAPHY 

the  point  of  origin  becomes,  the  more  will  the  shape  of  the  waves  resemble 
that  produced  by  a  simple  antenna. 

C.  The  Field  at  very  great  Distances  from  the  Antenna. — From  Arts. 
20a  and  25a,  the  following  may  be  concluded  in  regard  to  the  field  imme- 
diately above  the  earth's  surface,  at  distances  very  great  in  comparison 
to  the  wave-length: 

1.  The  direction  of  the  electric  lines  of  force  is  approximately  perpen- 
dicular to  the  earth's  surface,  that  of  the  magnetic  lines  parallel  to  it; 
both  are  perpendicular  to  the  direction  in  which  the  wave  moves. 

2.  The  electric  and  the  magnetic  fields  are  in  phase  [Art.  20d\. 

3.  The  amplitudes  of  the  electric  and  magnetic  field  strengths  are  ex- 
pressed by 

_  cA  .  |7.| 


3  X  1010  c.g.s.  units 

1^0  1  amp. 


X         rcm.        cms. 

ah      |7o| 

=  4-jr  -r-  -  -  -  c.g.s.  units 

A          T 


(i) 


where  h  represents  the  height  of  the  antenna,  /0  the  current  amplitude  at 
the  current  anti-node  of  the  antenna,  a  the  form  factor  of  the  antenna  and 
r  the  distance  from  it.  Accordingly,  the  amplitude  of  the  field  at  great 
distances  is  inversely  proportional  to  the  distance  r. 

d.  Penetration  of  the  Waves  into  the  Ground. — As  the  waves  spread  out 
over  the  earth's  surface,  they  penetrate  to  some  extent  into  the  ground, 
but  in  so  doing  their  amplitude  is  rapidly  decreased.  Thus  in  sea  water 
of  good  conductivity,*  at  a  depth  of  1  m.  the  amplitude  is  only  about  one- 
tenth  of  its  value  above  the  surface,  with  a  wave-length  of  about  700  m.* 

139.  Over  Flat  Ground  of  not  very  High  Conductivity  (A.  SOMMER- 
FELD). — If  the  earth's  surface  at  the  location  in  question  has  relatively 
low  conductivity,  as  is  the  case  even  with  fresh  water,  but  particularly 
with  dry  ground,  f  the  results  are  quite  different,  the  change  increasing  as 
the  conductivity  and  the  dielectric  constant  of  the  ground  decrease.221 
The  rule  given  in  Art.  138a  for  the  construction  of  the  field  then  no  longer 
applies  at  all.  The  appearance  of  the  field  in  the  vicinity  of  the  trans- 

*  Specific  conductivity  =  5  X  10~n  c.g.s.  units.  The  amplitude,  A,  at  a  depth 
Z,  is  of  the  form  A  =  A0erz  (A0  =  amplitude  at  the  surface). 

t  For  qualitative  consideration  the  specific  conductivity,  a  and  dielectric  constant, 
fc,  may  be  assumed  to  be  as  follows  :223 

Sea  water  <r  =  1  to  5  X  10~n  c.g.s.  units  k  =  80 

Fresh  water  =                  10~14  c.g.s.  units  =  80 

Wet  earth  =   10~13  to  10~14  c.g.s.  units  =  5  to  15 

Dry  earth  =  10~15  c.g.s.  units  =  2  to    6 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE  249 

mitter  is  not  known.  Nor  do  the  statements  made  in  Art.  138c  hold  good 
for  great  distances  from  the  transmitting  antenna. 

Instead  the  facts,  according  to  A.  SoMMERFELD's222  theory,  are  as 
follows: 

a.  Surface  and  Space  Waves. — The  waves  which  emanate  from  a  trans- 
mitter placed  in  a  homogeneous  insulating  material  were  discussed  in 
Art.  20.     They  are  characterized  by  the  fact  that  energy  is  radiated  in 
straight    lines,    radially    from    the    transmitter.*     Consequently,    the 

energy  varies  as  -y  (r  =  distance  from  source)  and  the  amplitudes  of  the 

electric  and  magnetic  field  strengths  vary  as  —    We  will  refer  to  these  as 

"space  waves"  in  what  follows. 

A  different  kind  of  wave  is  obtained,  e.g.,  with  LECHER'S  system  [Art. 
72c].  Here  the  waves  travel  along  the  wires,  following  any  bends  they 
may  have.  The  flow  of  energy  along  the  wires  and  the  amplitude  of  the 
waves  would  remain  constant  during  their  progress,  were  it  not  for  the 
fact  that  a  portion  of  the  energy  is  consumed  in  the  wires  (due  to  Joulean 
heat  developed).  This  causes  a  gradual  reduction  in  the  energy  and  wave 
amplitude  along  the  course  of  travel,  a  phenomenon  which  is  termed 
"absorption."  We  will  refer  to  waves  of  this  kind  as  "surface  waves," 
as  they  follow  the  surface  of  the  conductor. 

b.  The  wave  emanated  into  the  air  by  an  antenna  at  the  earth's  surface 
may  be  conceived  as  consisting  of  two  component  parts,  one  of  which  is  of 
the  nature  of  a  space  wave,  the  other  of  a  surface  wave.224*     In  the  former  the 

energy  oc  —  >    the  amplitude  therefore  «.-•   in  the  latter  the  energy  °c  -, 

the  amplitude  «  —=•     The  fact  that  in  the  latter  there  is  a  decrease  in  the 

Vr 

energy  as  the  distance  increases,  in  contrast  to  the  wave  following  a  wire 
— and  in  addition  to  and  entirely  aside  from  such  absorption  as  occurs — • 
is  explained  by  the  fact  that  the  energy  is  spreading  itself  out  over  ever- 
increasing  circles,  as  the  wave  travels  its  course. 

Absorption  of  course  occurs  in  addition  to  this  reduction  in  ampli- 
tude due  to  the  expansion  of  the  wave  in  space.  As  each  wave  advances 
through  the  air  it  is  accompanied  by  a  wave  in  the  ground.  And  as  the 
ground  always  has  more  or  less  conductivity,  the  moving  electric  field, 
constituting  the  wave,  results  in  the  formation  of  currents,  just  as  in  the 
wires  of  the  LECHER  system.  These  currents  consume  energy,  which  is 
drawn  from  that  of  the  waves  radiated  by  the  antenna,  so  that  an  absorp- 
tion occurs  in  this  way. 

c.  While  at  short  distances  from  the  transmitter,  the  waves  are  al- 

*  The  direction  of  the  flow  of  energy  is,  as  already  stated  previously,  perpendicular 
to  both  the  electric  and  magnetic  field  directions. 


250  WIRELESS  TELEGRAPHY 

most  entirely  of  the  nature  of  space  waves,  as  the  distance  increases  the 
surface  component  becomes  more  and  more  predominant,  as  its  amplitude 
decreases  more  slowly  than  that  of  the  surface  component.  That  is,  the 
nature  of  the  wave  constantly  approaches  that  of  a  surface  wave.* 

This  change  is  the  more  rapid,  the  shorter  the  wave-length  is  and  the 
lower  the  conductivity  and  dielectric  constant  of  the  ground  are.  A  cal- 
culation of  the  distance  at  which  the  actual  amplitude  of  the  wave  differs 
by  10  per  cent,  from  the  amplitude  of  the  space  wave,  results  in  the  fol- 
lowing figures: 

Sea  water f  X  =  2    km.  Distance  =  20,000  km.  approx. 

Sea  water  X  =  1     km.  Distance  =     5000  km.  approx. 

Sea  water  X  =  0.3  km.  Distance  =       500  km.  approx. 

Fresh  water  f  X  =  2     km.  Distance  =  4  km.  approx. 

The  distance  becomes  still  shorter  with  dry  ground. 

Hence,  while  with  sea  water  for  all  distances  which  come  into  consider- 
ation— 20,000  km.  is  half  the  circumference  of  the  earth — and  for  all 
wave-lengths  over  1  km.  the  waves  have  the  characteristics  of  space 
waves,  J  with  fresh  water  and  even  far  more  so  with  dry  ground,  they 
assume  the  characteristics  of  surface  waves  at  distances  of  only  a  few 
wave-lengths  or  even  less  than  one  wave-length.  Hence  the  nature  of 
the  wave  propagation  in  this  case  must  not  be  conceived  as  being  the 
same  as  that  described  in  Art.  138  over  sea  water. 

d.  The  subdivision  of  the  wave  into  a  space  wave  and  a  surface  wave 
and  a  wave  within  the  ground  [b]  makes  it  possible  to  give  a  simple 
description  of  the  phenomenon.  Physically,  there  is  of  course  only 
one  single  wave  extant,  which  travels  partly  through  the  air,  partly 
through  the  ground  along  its  upper  surface. 

The  appearance  of  the  electric  lines  of  force  of  this  wave  in  air  at  a 
given  instant  and  a  distance  of  30  to  30.5  wave-lengths  from  the  trans- 
mitter is  shown  diagrammatically  in  Figs.  297  and  298,  which  are  taken 
from  an  article  by  P.  EPSTEIN, 225  the  assumption  being  that  the  wave- 
length is  2  km.  and  that  the  conductivity  of  the  upper  stratum  of  the 

*  When  the  distance  becomes  very  great,  the  surface  wave  may  again  give  way  to 
the  space  wave,  as  the  former  is  more  rapidly  absorbed.  It  is  questionable,  however, 
whether  this  effect  is  of  practical  importance. 

f  On  the  assumption  that  a  =  10~n  c.g.s.  units  for  sea  water  and  10~14  c.g.s.  units 
for  fresh  water. 

J  Herein  lies  the  justification  for  the  statements  in  Art.  138.  The  electric  and 
magnetic  field  strengths  in  this  case,  taking  consideration  of  the  absorption,  are 
given  by  [Art.  138c]: 

E0  =  47T  ~  •  1/0| •  3  X  1010  c.g.s.  units 

A  T 

,       <**>  r    i  €  ~  ^ 

MQ  =  47T  —  -  l/o  I c.g.s.  units 

A  / 

in  which  /3  is  the  coefficient  of  absorption. 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE  251 


30.0 


30J 


+1* 


y/////////////////////////////////////^^^ 


3O.25 

FIG.  298. 


W, 
30L5 


252 


WIRELESS  TELEGRAPHY 


ground  is  about  midway  between  that  of  sea  water  and  wet  ground. 
The  scale  of  the  ordinates  (heights  above  ground)  is  one-twelfth  of  that 
of  the  abscissae  (distances  from  transmitter)  in  these  figures. 

By  way  of  comparison,  Fig.  299  represents  the  lines  of  force  which 
would  correspond  to  an  infinitely  great  conductivity  of  the  ground,  ac- 
cording to  Art.  138,  the  same  scale  and  distance  being  used  as  in  the  pre- 
ceding figures.  It  will  be  noted  that  there  is  no  very  great  difference 
between  Fig.  299  and  the  other  Figs.  297  and  298;  the  latter,  however, 
are  based  on  the  assumption  of  relatively  high  ground  conductivity. 
With  dry  ground  the  differences  would  be  much  more  marked. 


30.25 

FIG.  299. 


30.5 


e.  The  nature  of  the  field  of  the  wave  immediately  above  the  earth's 
surface  at  very  great  distances  from  the  transmitter,  is  of  special  practical 
interest.  If  the  earth's  surface  were  as  good  a  conductor  as  a  metal, 
then  [Art.  138] 

1.  The  electric  field  would  be  exactly  perpendicular,  the  magnetic 
field  parallel  to  the  earth's  surface,  and 

2.  Both  would  be  in  phase  [Art.  137]. 

As  a  matter  of  fact  these  conditions  are  approximately  true  over  sea 
water,  but  they  do  not  hold  for  fresh  water  or  dry  ground  (J.  ZENNECK22). 

However,  the  direction  of  the  magnetic  lines  of  force  remains  parallel  to 
the  earth's  surface,  but  the  electric  field  instead  of  being  perpendicular 
to  the  earth's  surface  tends  to  follow  the  direction  of  travel  of  the  wave.* 
Hence  to  the  component,  Ez,  of  the  electric  field  strength  perpendicular 
to  the  earth's  surface  there  comes  an  additional  component,  EXJ  in  the 

*  This  is  already  noticeable  in  Figs.  297  and  298,  even  though  not  very  prominent, 
as  the  conductivity  and  wave-length  were  assumed  to  be  relatively  high  for  these 
figures. 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE  253 

direction  parallel  to  the  earth's  surface.  The  ratio  between  the  amplitudes 
of  these  two  components  is  shown  by  the  full  line  curves  of  Fig.  300  for 
different  values  of  the  conductivity  and  the  dielectric  constant,*  under 
the  assumption  that  the  distance  from  the  transmitter  is  so  great  that  the 
waves  may  be  considered  not  merely  as  surface  waves,  but  as  plane  waves. 
From  the  curves  it  is  evident  that  when  the  dielectric  constant  is  small, 
the  horizontal  component  can  assume  quite  large  proportions. 


Log$=- 


-17 


d    W9        IO10      IO11        W12       IO12      it1*       IO15        IO16      IO17 

FIG.  300. 

In  this  case,  while  the  magnetic  field  and  the  vertical  component  of 
the  electric  field  are  approximately  in  phase  with  each  other,  there  is  a 
phase  difference,  <pt  between  the  horizontal  and  vertical  components  of 
the  electric  field  strength,  The  variation  of  this  phase  difference  is 
shown  by  the  dotted  curves  of  Fig.  300,  under  the  same  assumptions 
made  for  the  full  line  curves. 

The  result  is  that  the  electric  field  is  no  longer  a  pure  alternating  field 
but  possesses  a  more  or  less  large  rotating  field  component. 

A  comprehensive  picture  of  the  field  can  be  obtained  by  the  familiar 
method  of  representing  the  resultant  field  strength  by  means  of  a  vector. 

*  N  -  5  X  IO5  cycles  per  sec.,  X  =  approx.  670  m. 


254 


WIRELESS  TELEGRAPHY 


The  locus  of  the  end  of  the  vector  during  one  cycle  is  then  an  ellipse,  of 
which  (see  Fig.  301). 

QB        E^     OAi  _  O£i  _ 

OA  ==  #*<,'   OA    ~  OB  a<P 

For  the  typical  cases  of  low  ground   conductivity,  the  curves  rep- 
resenting the  field  in  the  air  acquire  the  form  of  Fig.  302*  or  Fig.  303. f 

While  the  field  over  sea  water,  according  to  Art.  138c, 
is  practically  a  pure  vertical  alternating  field,  over  dry 
ground  the  field  is  greatly  inclined  at  an  angle  to  the  vertical 
and  has  a  more  or  less  prominent  rotating  component.221 

f.  The  falling  off  in  amplitude  during  the  progress  of 
the  waves,  depends  upon  the  conductivity  and  dielec- 
tric constant  of  the  ground  and  to  a  particularly  great 
extent  upon  the  wave-length.     The  greater  the  conduc- 
tivity and  dielectric  constant  of  the  earth,  the  slower  is 
the  falling  off  in  amplitude,  other  things  being  equal; 
hence  it  is  slow  over  sea  water,  very  rapid  over  dry 
ground.     The  relation  to  the  wave-length  is  such  that  the  distance  at 
which  the  amplitude  has  fallen  to  a  given  fraction  of  its  value  in  the 

immediate  vicinity  of  the  transmitter  °c  —  over  ground    of    very  good 


FIG.  301. 


FIG.  302. 


FIG.  303. 


conductivity  (sea  water)  and  approximately  oc  -  over    dry    ground    of 

very  low  conductivity. 

This  relation  to  the  wave-length  is  very  clearly  illustrated  by  the 
curves  of  Fig.  304,  in  which  the  falling  off  of  the  amplitude  along  the 
length  of  a  quadrant  of  the  earth's  circumference  is  shown,  the  ordinates 


*  Assumption  N  =  5  X  105  cycles  per  sec.,  k  =  2,  <r  =  10~15  c.g.s.  uni 
f  Assumption  N  =  5  X  105  cycles  per  sec.,  k  =  2,  <r  =  10~16  c.g.s.  uni 


units, 
c.g.s.  units. 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE   255 

being  the  products  of  the  amplitudes  and  their  respective  distances 
from  the  transmitter. 

From  what  has  preceded  the  following  practical  conclusions  may  be 
drawn : 

1.  Great  wave-length  is  far  more  advantageous  for  the  propagation  of  the 
waves  than  short  wave-length.*  Thus  in  telegraphing  across  the  sea, 
the  same  reduction  in  amplitude  occurs  at  a  distance  twenty-five  times 
as  great  with  a  5  km.  wave  as  with  a  1  km.  wave. 


2.  The  falling  off  in  amplitude  is  much  greater  over  land  than  over  sea 
for  the  same  distance,  the  difference  becoming  more  marked  as  the  wave 
length226  employed  becomes  shorter.  Hence,  if  waves  are  traveling  partly 
over  land  and  partly  over  sea,  then  only  a  few  miles  over  land  may  cause 
the  same  reduction  in  amplitude  as  several  hundred  miles  over  sea. 
Hence,  where  large  distances  over  sea  are  to  be  bridged  (as  in  trans- 
atlantic work,  ship-and-shore  work) ,  it  is  of  the  greatest  importance  to 
erect  the  shore  stations  as  near  the  water  as  possible,  f 

g.  The  velocity  of  propagation  of  the  waves  as  measured  along  the 
earth's  surface  may  be  somewhat  greater  than  the  velocity  of  light, 
3  X  1010  cm.  per  sec.  =  300,000  km.  per  sec.,  but,  just  as  over  sea  water,  the 
difference  is  never  great.221 

140.  Effect  of  the  Spherical  Shape  of  the  Earth.— (H.  POINCAKE, 
J.  W.  NICHOLSON)  . — The  various  relations  brought  out  in  Arts.  138  and 
139,  rested  on  the  assumption  that  the  conductor  (the  earth),  upon  which 
the  transmitter  stands,  has  a  plane  surface.  Consequently  they  hold 

*  So  far  as  the  influence  of  the  earth's  surface  is  concerned.  The  effect  of  the 
atmosphere  [Art.  145]  is  not  taken  into  consideration  here. 

f  In  this  respect  the  high-power  stations  at  Clifden  and  Glace  Bay,  also  the  Nord- 
deich  station  are  well  located,  while  the  Eiffel  Tower  and  Nauen  Stations  are  rela- 
tively at  a  disadvantage. 


256  WIRELESS  TELEGRAPHY 

approximately  for  such  distances  in  which  the  earth's  surface  may  be 
considered  as  practically  plane,  but  no  longer  apply  to  transatlantic 
stations,  for  which  distances  of  about  one-eighth  the  earth's  circumference 
are  involved. 

How  these  relations  change  because  of  the  spherical  form  of  the 
earth  has  been  theoretically  considered  by  the  authors  named  above, 
for  the  ideal  case  of  extremely  high  conductivity  of  the  earth's  surface. 
H.  W.  MARCH226  has  come  to  the  same  conclusions  in  a  simpler  way. 

These  results  may  be  generalized  under  the  statement  that  the  earth's 
curvature  affects  the  conditions  which  would  exist 

Transmitter  ,  , 

over   the  previously  assumed  plane  surface  in  two 
ways,  viz., 

1.  In   that   the   energy   propagation   along   the 
curved  surface  is  different  than  along  a  plane  surface. 

2.  In  that  the  radiated  or  propagated  energy  does 
not  entirely  follow  the  course  of  the  earth's  curva- 
ture,  or   to   express   this  differently,   in  that   there 

FIG.  305.  takes  place  in  addition  to  the  propagation  along  the 

earth's  surface,  a  radiation  or  "straying"  of  some  of 
the  energy  into  space  away  from  the  earth's  surface. 

a.  Let  us  first  consider  the  propagation  along  the  earth's  curvature 
entirely  aside  from  the  "  stray  "  energy.  The  nature  of  this  propagation 

is  such  that  instead  of  the  amplitude  varying  as  - ,  as  was  the  case  with  a 
plane,  highly  conducting  surface  [Art.  138c],  the  amplitude  in  this  case 


in  which  r  is  the  distance  from  the  transmitter  measured  along  the  earth's 
curvature  and  &  the  angle  at  the  center  of  the  earth  enclosing  the  arc 
whose  length  is  r  (Fig.  305). 

This  variation  in  amplitude  is  shown  by  the  full  line  curve  of  Fig.  306, 
for  distances  up  to  half  the  earth's  circumference  (#  =  0°  to  180°), 
the  dotted  curve  showing  the  falling  off  in  amplitude  when  this  varies  as 

— ,  i.e.j  for  a  plane,  highly  conductive  ground.     Hence,  if  there  were  no 

stray  field,  the  amplitude  would  decrease  less  rapidly  over  the  spherical 
earth's  surface  than  in  the  case  of  the  flat  surface.  The  difference,  how- 
ever, is  not  very  great  for  distances  up  to  a  quadrant  of  the  earth's 
circumference,  and  at  half  a  quadrant  amounts  to  only  5.4  per  cent. 

The  fact  that  the  amplitude  decreases  less  rapidly  in  this  case  than 
over  a  plane  surface,  that,  in  fact,  if  there  were  no  straying,  it  would 
begin  to  increase  again  after  a  considerable  distance  from  the  transmitter, 
can  be  accounted  for  by  a  consideration  of  the  geometric  distribution  of 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE  257 


the  flow  of  energy  along  the  earth's  surface.*  Its  course  is  along  the 
meridians  drawn  through  the  transmitter,  while  in  the  case  of  the  flat 
surface  it  is  along  the  radii  in  its  plane  and  passing  through  the  base  of 
the  antenna.  The  latter  continue  to  diverge  at  a  constant  angle  as  the 
distance  increases,  so  that  the  energy  is  spread  out  over  a  constantly 
increasing  area.  With  the  spherical  surface,  however,  the  meridian 
circles  diverge  only  between  the  values  &  =  0°  and  &  =90°,  i.e.,  over  the 


1G 


J 


15  SO   45  60   75  90  105  120  135  ISO  165  180° 

— *d 

FIG.  306. 

length  of  one  quadrant.  Moreover,  even  within  these  limits  the  angle 
of  divergence  grows  constantly  smaller  as  the  distance  increases;  hence 
the  area  over  which  the  energy  spreads  does  not  increase  as  rapidly  as 
in  the  case  of  the  plane  surface.  As  the  distance  is  further  increased, 
from  #  =  90°  to  &  =  180°,  the  meridians  converge  until  they  again 
intersect  at  a  point  diametrically  opposite  the  antenna;  so  that  here  we 
have  a  gradual  concentration  of  the  flow  of  energy  as  the  opposite 
pole  is  approached. 

b.  In  view  of  the  straying  of  energy  the  expression  given  in  a  is  incom- 
plete without  the  so-called  stray  energy  factor,  which  has  been  theoretically 
shown  to  be  equal  to 

-0.36.*.V^t  -0.0019. -5-^- 

e  =  e  vx(r  and  Xinkm.) 

*  This  alone,  however,  does  not  determine  the  reduction  in  amplitude  with  in- 
creasing distance,  but  rather  the  flow  of  energy  through  the  entire  space. 

f  a  =  radius  of  the  earth.     The  factor  0.0019  ,  —^=.  might  be  termed  the  "stray 

energy  coefficient.'1 
17 


258  WIRELESS  TELEGRAPHY 

so  that  the  equation  for  the  variation  in  the  amplitude,  A,  over  the 
curved  surface  of  the  earth  having  infinitely  great  conductivity  and 
surrounded  by  a  homogeneous  absolutely  non-conducting  atmosphere 
[Art.  145]  becomes 

1        /   #         -0.0019. -^p 

A=A0.±.J-?-=.e  V*  (1) 

r      \  sin  & 

Thus,  e.g.,  for  r  =  %  earth's  quadrant  and  X  =  4  km.,  the  stray  energy 
factor  becomes  Moo- 

c.  A  comparison  of  this  equation  with  that  deduced  by  L.  W.  AUSTIN 
[Art.  1466]  from  his  daylight  measurements,  shows  that  the  results 
obtained  by  the  two  methods  do  not  differ  very  greatly,  both  as  to  the 
quantitative  value  of  the  stray  energy  factor  and  as  to  the.  relation  of 
this  factor  to  the  wave-length. 

Moreover,  a  comparison  of  Austin's  actual  observations  with  the 
theoretical  equation  (1)  leads  to  the  conclusion  that  these  observations 
are  reproduced  just  as  closely  by  the  theoretical  equation  as  by  his 
empirical  formula. 

At  the  same  time  it  must  be  remembered  that  the  theory  involved 
has  not  yet  been  completed.  It  has  been  developed  only  under  the 
assumption  that  the  earth's  surface  has  infinitely  great  conductivity. 
It  remains  to  be  seen  whether  a  completed  theory,  taking  consideration 
of  the  finite  conductivity  of  the  earth's  surface  and  therefore  involving  a 
reduction  in  amplitude  due  to  absorption,  will  be  in  equal  accord  with 
test  observations. 

2.  WAVE    PROPAGATION    OVER   UNEVEN    OR   NON-HOMOGENEOUS 

GROUND 

In  1  it  was  assumed  that  the  portion  of  the  earth's  surface  over 
which  the  waves  pass  consisted  of  homogeneous  material  and  that  the 
surface  was  a  smooth  plane  or  sphere.  There  remains  to  be  investigated 
what  changes  occur  if: 

1.  The  earth's  surface  is  considerably  uneven. 

2.  Underneath  the  surface  there   are  strata  of  widely  varying  con- 
ductivity and  dielectric  constants. 

3.  The  earth's  surface  has  portions  varying  greatly  in  their  con- 
ductivity and  dielectric  constants. 

141.  Uneven  Surfaces. — The  waves  in  their  course  may  encounter 
obstacles  in  the  form  of  hills  or  mountains  and  trees  or  buildings. 

a.  With  hills  or  mountains,  three  possible  cases  can  be  distinguished, 
viz., 

1.  The  wave  passes  through  the  hill  (Fig.  307); 

2.  It  glides  over  the  contour  of  the  hill  (Fig.  308) ;  or 

3.  The  waves  bend  down  over  the  peak  of  the  hill  to  reach  the  farther 
side  (Fig.  309). 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE  259 

Just  what  takes  place  in  any  individual  case  depends  upon  the  form 
of  the  hill  and  the  conductivity  and  dielectric  constant  of  its  material. 
Bending  probably  occurs  in  all  cases.  That  it,  in  fact,  frequently  plays 
the  main  part  follows  from  the  observations  of  H.  B.  JACKSON227  who 
found  that  a  ship  lying  just  alongside  of  a  hill  could  not  receive  the 


FIG.  307. 


FIG.  308. 


FIG.  309. 

messages  sent  from  a  station  located  on  the  other  side  of  the  hill,  but 
did  receive  them  as  soon  as  it  had  passed  somewhat  further  away  from 
the  hill.  If  the  hill  in  the  path  of  the  waves  consists  of  material  of 
relatively  good  conductivity  and  its  width  is  very  great  compared  to 
the  wave-length,  the  result  will  probably  be  mainly  as  described  in  case 


260  WIRELESS  TELEGRAPHY 

2.  The  portion  of  the  wave  passing  through  the  hill  (case  1)  can  only  be 
of  consequence  when  the  material  of  the  hill  has  very  low  conductivity 
(rocks)  and  the  hill  is  not  very  wide. 

In  all  cases  the  hill  will  decrease  the  amplitude  of  that  portion  of 
the  wave  which  passes  through  or  over  it,  that  is,  the  hill  will,  so  to  say, 
throw  an  electromagnetic  shadow,  which  will  be  more  marked  the  shorter 
the  wave-length  is.* 

This  has  been  observed,  e.g.,  in  tests  between  Nauen  and  ships  on  the 
Atlantic  in  which  the  "  shadow  "  of  the  mountains  of  Spain  was  distinctly 
evident.  In  practice  the  range  of  portable  sets  in  mountainous  country 
is  usually  assumed  to  be  only  50  per  cent,  of  the  normal  range  on  flat  or 
only  slightly  hilly  country. 

b.  DUDDELL  AND  TAYLOR228  have  demonstrated  that  groups  of  trees 
may  very  greatly  interfere  with  the  distribution  of  short  waves.  Densely 
wooded  regions  are  particularly  unfavorable  to  the  propagation  of  short 
waves  and  it  is  usually  estimated  that  they  will  reduce  the  range  of 
portable  stations  by  50  per  cent.  Similarly  high  buildings  or  other 
structures,  especially  if  they  are  in  the  immediate  vicinity  of  the  trans- 
mitter or  receiver,  are  apt  to  be  a  great  hindrance.  In  both  cases,  no 
doubt,  it  is  a  question  of  the  effect  of  induced  currents. 

142.  Rain  and  Ground  Water  (F.  HACK229). — a.  The  case  previously 
mentioned  in  which  the  ground  consists  of  layers  having  very  different 
properties  closely  following  each  other,  exists  when  the  upper  layer  of  a 
portion  of  ground  which  has  very  low  conductivity  and  low  dielectric 
constant,  becomes  highly  conductive  and  has  a  high  dielectric  constant 
due  to  a  rain  or  snow  fall  of  long  duration.  This  case  has  been  pre- 
viously treated  only  on  the  assumption  that  the  distance  from  the  trans- 
mitter was  very  great,  so  that  the  waves  could  be  considered  not  merely 
as  surface  waves,  but  also  as  plane  waves. 

The  direction  of  the  electric  field  at  the  earth's  surface  under  this  as- 
sumption is  shown  in  Figs.  310  to  312.f  The  first  represents  the  field 
[see  Art.  39e]  for  entirely  dry  ground,  the  second  and  third  represent  the 
case  of  the  ground  being  wet  to  a  depth  of  20  and  40  cm.  respectively. 
From  these  figures  it  is  evident  that  the  large  rotating  field  component 
which  is  present  when  the  ground  is  quite  dry,  becomes  more  and  more 

*  MARCONI191  has  stated  that  the  weakening  of  the  waves  by  hills  or  mountains, 
if  the  waves  are  relatively  short,  occurs  only  in  daylight,  and  never  at  night. 

f  Thanks  are  due  PROF.  DR.  F.  HACK  of  Stuttgart  for  the  Figs.  310  to  317.  They 
are  based  on  the  assumptions  that: 

For  dry  ground,       a-  =  10~16  c.g.s.,         k  =    2 

For  wet  ground        a-  =  10~13  c.g.s.,         k  =  15 

For  ground  water,  a  =  5  X  10~14  c.g.s.,         k  =  80 

The  curve  drawn  in  the  shaded  area  represents  the  electric  field  in  the  part  of  the 
ground  under  consideration. 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE   261 
^  =2000  77i.  •#-  2000  m.  Jl^ZOOO  m,. 


."' 


T=0m. 
FIG.  310. 


/ 


FIG.  311. 


FIG.  312. 


Jl-ZOOOm,. 


0 


JL- 2000m. 


FIG.  313. 


FIG.  314. 


T=10m. 
FIG.  315. 


=  zooom. 


FIG.  316. 


T  =  200  771. 
FIG.  317. 


262  WIRELESS  TELEGRAPHY 

reduced  so  that  the  field  approaches  a  pure  alternating  field,  as  the  wet 
layer  of  the  soil  increases  in  depth. 

The  absorption  of  the  waves  is  also  affected  by  rain;  the  deeper  the  rain 
soaks  into  the  ground  the  more  the  absorption  is  decreased. 

6.  In  most  localities,  the  upper  layer  of  dry  soil  and  stones  has  a  stratum 
of  ground  water  at  a  depth  of  from  just  a  few  to  about  100  m.  below 
the  surface. 

Figs.  313  to  317,  drawn  under  the  same  assumptions  which  Figs.  310 
and  312  were  based  upon,  illustrate  the  field  at  the  earth's  surface 
for  a  wave-length  of  2000  m.  for  various  distances,  T,  of  the  ground  water 
below  the  surface.  In  all  cases  the  ground  water  is  assumed  to  extend 
to  a  very  great  depth.  It  will  be  seen  that  the  effect  of  the  ground  water 
is  to  bring  the  direction  of  the  electric  field  more  nearly  vertical  to  the 
surface  of  the  earth.  The  absorption  may  be  either  increased  or  decreased, 
but  in  most  practical  cases  where  the  wave-length  is  greater  than  1  km. 
it  is  reduced. 

143.  Distribution  Over  Land  and  Water. — If  there  are  both  land  and 
water,  particularly  sea  water  between  two  stations,  various  effects  may 
occur. 

a.  The  main  portion  of  the  wave  may  be  guided  by  the  stretch  of  sea 
water,  following  this  rather  than  a  shorter  land  route,  e.g.,  it  is  not  im- 
possible that  when  English  coast  stations  transmit  to  ships  in  the  Medi- 
terranean Sea,  a  portion  of  the  waves   reaching  the  ships,  instead  of 
taking  the  direct  path  across  the  Alps,  pass  entirely  over  sea,  by  way  of 
Gibraltar.* 

Even  rivers  seem  to  have  a  similar  effect.  At  any  rate  in  tests  made 
on  moving  trains  it  was  found  that  the  intensity  of  the  signals  received  al- 
ways greatly  increased  when  the  train  approached  a  river.230  Hence 
it  would  seem  that  the  waves  tend  mainly  to  follow  the  better  conducting 
water  paths. 

Moreover,  in  tests  with  such  receiving  antennae  as  determine  the  direc- 
tion of  the  incoming  waves  [Art.  2076],  it  was  noticed  that  the  direction 
did  not  always  correspond  with  that  of  the  transmitter.231  The  waves 
in  such  cases,  evidently  under  the  influence  of  the  variations  in  the  ground, 
did  not  proceed  in  straight  lines  over  the  surface  of  the  earth. 

b.  In  passing  from  water  to  land  and  vice  versa]  a  partial  reflection 

*  This  would  not  explain  the  fact,  observed  by  MARCONI191  that  ships  in  the 
Mediterranean  could  telegraph  most  conveniently  with  English  land  stations  at 
night  (X  =  300  or  600  m.),  at  distances  over  1000  miles,  but  that  ships  in  the  North 
Atlantic  Ocean  can  very  rarely  be  reached  at  the  same  distances,  though  no  land 
intervenes  here.  [Translator's  Note. — Similar  observations  have  been  made  on  the 
American  coast  and  from  many  reports  it  would  appear  that  usually  longer  distances 
can  be  attained  in  a  north  and  south  than  in  an  east  and  west  direction.] 

t  Or  expressed  in  more  general  terms — in  passing  between  portions  of  the  earth's 
surface  having  different  electric  properties. 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE  263 

and  possibly  also  refraction  or  bending  of  the  waves  must  occur.232 
Hence  the  amplitude  of  the  waves  received  from  a  given  transmitter  at 
a  given  distance  depends  not  merely  upon  the  distance  traveled  over 
land  and  over  sea,  but  also  upon  the  shape  of  the  coast*  encountered  by 
the  advancing  waves. 

Perhaps  this  accounts  for  the  fact  that  at  times  certain  points  at 
a  much  greater  distance  from  the  transmitter  receive  its  signals  much 
louder  than  points  nearer  to  it.  In  many  such  cases,  however,  the 
explanation  may  lie  in  the  possible  interference  between  two  trains  of 
waves  which  have  reached  the  point  of  reception  by  different  paths  and 
are  therefore  out  of  phase  with  each  other. 

3.  EFFECT  OF  ATMOSPHERIC  AND  OTHER  INFLUENCES  UPON  THE 

WAVES 

144.  Effect  of  the  Condition  of  the  Atmosphere. — a.  The  entire  theory 
discussed  in  what  has  preceded  does  not  entirely  represent  the  actual 
conditions;  it  was  based  upon  the  assumption  that  the  earth,  itself  a 
conductor,  is  surrounded  by  a  perfect  insulating  and  homogeneous 
medium.  However,  the  properties  of  the  atmosphere  undoubtedly  vary 
at  different  heights  and  furthermore  the  air  is  not  a  perfect  insulator. 
These  conditions  must  be  factors  in  determining  the  propagation  of  the 
waves. 

b.  The  absorption  of  the  waves  may  depend  upon  the  condition  of 
the  atmosphere.     Moreover  the  direction  and  the  form  of  the  waves  may 
be  changed  if  there  are  a  number  of  layers  of  the  atmosphere,  having 
different  qualities,  spread  over  the  surface  of  the  earth.     Finally,  any 
heterogeneity  of  the  atmosphere  may  cause  dispersion,  refraction  or  partial 
reflection. 

The  similar  phenomena  which  occur  when  rays  of  light  pass  through 
the  atmosphere  have  often  been  used  as  analogies.223  This  is  justified 
within  certain  limits,  but  the  wide  difference  between  the  two  cases  must 
not  be  forgotten.  Thus,  the  wave-length  used  in  radio-telegraphy  for 
the  longer  distances  is  from  1000  to  6000  m.  A'ny  heterogeneity  in 
the  atmosphere  extending  over  one  or  more  kilometers  is,  therefore,  al- 
ready of  the  same  order  of  size  as  the  wave-length;  the  conditions  are  then 
comparable  to  those  encountered  in  optics  in  colloidal  solutions.  Further- 
more, not  merely  the  condition  of  the  atmosphere,  but  also  the  proximity 
to  the  earth's  surface  in  a  given  case  determines  the  nature  of  the  propaga- 
tion of  electromagnetic  waves,  wherein  another  difference  exists  as  com- 
pared to  light  waves. 

c.  There   is   no   doubt   at   all   that   atmospheric   conditions   greatly 
influence   the  range   of  a  station.     But   we  must  make   the  following 
distinction: 

*  Thus  a  circular  bay  might  perhaps  act  similarly  to  a  concave  mirror. 


264  WIRELESS  TELEGRAPHY 

1.  The  direct  effect,  which  the  condition  of  the  air  (ionization,  hu- 
midity, atmospheric  pressure  and  temperature)  may  have  upon  the  wave 
propagation. 

2.  The  indirect  effect  which  may  consist,  on  the  one  hand,  of  changes 
in  the  insulation  and  ground  resistance  in  the  vicinity  of  the  transmit- 
ting antenna  and  hence  in  the  oscillations  radiated;  on  the  other  hand 
changes  in  the  earth's  surface  between  transmitter  and  receiver  affecting 
the  absorption  of  the  waves.234 

Accordingly,  experiments  in  which  these  indirect  effects  were  not 
avoided  or  at  least  were  not  under  exact  control,  are  of  no  use  in  deter- 
mining the  direct  effects.  This  immediately  eliminates  all  tests  over 
land,  as  it  is  impossible  to  avoid  or  quantitatively  determine  the  effect 
of  the  weather  upon  the  stretch  of  the  earth's  surface  in  question.  Only 
tests  over  sea,  and  preferably  from  ship  to  ship  should  be  considered, 
and  even  these  only  if  it  is  definitely  determined  that  the  insulation  of 
the  antenna,  and  hence  the  oscillations,  were  not  affected. 

In  spite  of  all  such  precautions,  the  greatest  care  is  necessary  in 
drawing  conclusions  from  the  results  obtained.  If  the  atmospheric 
conditions  really  do  influence  the  wave  propagation,  then  the  entire  zone 
of  space  between  transmitter  and  receiver  must  be  taken  into  con- 
sideration, something  hardly  possible  in  most  such  tests  over  great 
distances. 

145.  lonization  of  the  Atmosphere. — In  previous  articles  the  air  was 
assumed  to  be  a  perfect  insulator.  However,  the  air  is  always  some- 
what ionized,  due  to  radio-active  emanations  from  the  ground,  to  the 
action  of  the  sun's  ultra-violet  rays  and  probably  also  to  electrons  sent 
out  from  the  incandescent  sun.* 

a.  The  conductivity  of  the  atmosphere,  due  to  this  ionization,  up  to 
heights  accessible  by  means  of  balloons  (about  6000  m.)  is  very  low,  much 
lower  in  fact  than  that  of  the  dryest  ground.  Such  slight  conductivity 
can  hardly  have  an  appreciable  influence  upon  the  form  of  the  waves; 
their  absorption  is  probably  increased  by  it,  but  only  very  slightly.221 

However,  even  at  heights  attainable  in  balloons  it  is  noticeable  that 
the  ionization  of  the  air  increases  with  great  rapidity  as  the  height  in- 
creases. It  is  very  probable  that  it  assumes  large  proportions  at  very 
great  heights,  for  at  such  altitudes  the  action  of  the  ultra-violet  rays  of 
the  sun  and  probably  of  the  action  of  the  electrons  emanating  from  the 
sun  must  be  much  more  powerful  than  at  the  lower  layers  of  air,  where 
both  are  already  almost  entirely  absorbed. 

There  are  then  two  possibilities.  Either  the  conductivity  of  the 
air  even  at  the  greatest  altitudes  in  question,  is  still  very  small  as  com- 
pared to,  say,  the  conductivity  of  wet  ground;  in  which  case  the  effect  of 

*  It  has  been  reported236  that  the  polar  lights  have  a  marked  effect  upon  the  trans- 
mission between  a  station  in  Spitzbergen  and  one  in  Hammerfest. 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE  265 

the  upper  layers  of  the  atmosphere  will  consist  mainly  in  increased 
absorption  of  the  waves.  Or  the  conductivity  of  the  uppermost  layers 
of  the  atmosphere  is  of  about  the  same  order  as  that  of  wet  ground;  in 
which  case  the  conditions  would  be  quite  different  than  has  been  as- 
sumed in  Art.  138  et  seq.  We  then  would  not  have  a  practically  homo- 
geneous medium  of  infinitesimal  conductivity  surrounding  the  earth, 
but  rather  three  concentric  layers,  viz.,  the  earth's  crust  or  outer  layer 
of  relatively  good  conductivity,  then  the  lower  portion  of  the  atmosphere 
of  infinitesimal  conductivity  and,  finally,  the  upper  layers  of  the  at- 
mosphere of  good  conductivity,2260  the  transition  between  the  latter  two 
being  more  or  less  gradual.  In  this  case,  the  waves  radiated  by  a  trans- 
mitter at  the  earth's  surface  would  find  two  guiding  conductive  layers 
and  would  progress  in  the  space  between  them.  The  form  of  the  waves, 
moreover,  might  become  quite  different  than  that  which  results  under 
the  assumptions  of  Arts.  138  and  139.  No  general  conclusion  can  be 
drawn  as  to  the  effect  of  the  upper  layers  of  the  atmosphere  upon  the 
absorption,  as  this  might  be  either  increased  or  decreased  according  to  the 
conductivity  of  the  upper  layers  of  the  air. 

b.  J.  A.  FLEMING237  considers  an  indirect  effect  of  the  atmospheric 
ionization.     He  assumes  that  in  the  upper  ionized  regions  of  the  atmos- 
phere, water  vapor  condenses  on   the  ions   thereby  increasing  the  di- 
electric constants  of  these  layers  and  so  reducing  the  velocity  of  the 
wave  propagation.     The  result  of  this  would  have  to  be  a  bending 
backward  of  the  wave  front  advancing  over  the  earth's  surface  and  the 
direction  of  the  radiation  would  thereby  be  turned  upward. 

c.  If  such  extensive  ionization  of  the  air  as  to  materially  affect  the 
waves,  either  directly  or  indirectly  is  at  all  possible,  then  it  must  be  kept 
in  mind  that  vertical  air  currents,  clouds,  fog,  etc.,  would  cause  wide 
variations  in  the  conductivity  at  different  parts  of  the  same  layer  of  air 
at  the  same  height.     Such  lack  of  homogeneity  might  furthermore  cause 
dispersion,  reflection,  absorption,  etc.,  of  the  waves  and  possibly  also  lead 
to  interference  phenomena.238 

d.  The  first  observation  which  indicated  an  effect  of  atmospheric  ion- 
ization, was  that  made  by  MARCONI, 239  which  has  since  then  been  re- 
peated again  and  again,  namely,  it  is  found  that  in  telegraphing  over  great 
distances,   but  with  not  very  great  wave-lengths   (X  <  4000  m.),   the 
same  transmitter  is  apt  to  be  much  more  effective  at  night  than  in  daylight. 
The  distance  reached  at  night  is  at  times  two  and  one-half  times  that 
reached   in   the   daytime,   according    to    MARCONI.     The  quantitative 
measurements  of  L.  W.  AUSTIN*  confirm  a  daylight  effect  and  agree 
with  MARCONI'S  observations  inasmuch  as  the  action  or  intensity  is  very 
nearly  constant  in  the  daytime,  but  very  irregular  at  night,  sometimes  being 
only  slightly  greater,  then  again  very  much  greater,  than  in  the  day.* 

*  AUSTIN'S  observations  [Art.  1466]  were  made  with  wave-lengths  up  to  3750  m. 


266  WIRELESS  TELEGRAPHY 

In  addition  there  have  recently  been  made  numerous  observations 
indicating  that  during  an  eclipse  of  the  sun  the  intensity  of  wireless 
signals  increased  as  the  sun  was  darkened  and  decreased  again  with 
increasing  sunlight.240 

These  observations,  so  far  as  reduced  daylight  intensity  is  concerned, 
would  be  explained  by  the  increased  ionization  of  the  upper  layers  of  the 
atmosphere  in  the  daytime.  Nor  would  MARCONI'S  observation  that  the 
difference  between  day  and  night  practically  disappears  with  wave-lengths 
of  6000-8000  m.  interfere  with  this  explanation;  for  it  might  well  be  that 
the  direct  [a]  or  the  indirect  [6]  effect  of  atmospheric  ionization,  as  well  as 
the  effect  of  the  conducting  earth,  is  not  so  great  for  long  as  for  short 
waves.  But  as  regards  MARCONI'S  statement  that  with  an  8000  m.  wave 
the  range  is  greater  in  the  day  than  at  night,  it  will  be  necessary  to  sub- 
stantiate this  with  observations  of  a  further  regular  increase  in  range  in  the 
daytime  with  additional  increases  in  wave-length,  before  drawing  any 
final  conclusions. 

It  will  be  difficult,  with  our  present  knowledge  of  the  conditions  in- 
volved, to  find  a  sound  explanation  for  the  observation  that  the  intensity 
of  signals  greatly  fluctuates  at  night.  *  This  observation  makes  the  gener- 
ally accepted  theory  that  the  night  action  is  the  normal  one,  correspond- 
ing to  an  unionized  atmosphere,  while  the  daytime  action  is  weakened 
directly  or  indirectly  by  ionization,  appear  somewhat  doubtful.  At  any 
rate,  it  is  possible  to  conceive  that  it  is  the  daytime  action  which  is 
"normal"  and  that  at  night  the  intensity  is  increased  by  causes  as  yet  not 
definitely  understood.  This  last  conception  would  be  the  only  possible 
one,  if  it  is  really  found  [Art.  140c]  that  the  falling  off  in  amplitude  actually 
observed  in  the  daytime  is  equal  to  that  theoretically  calculated  as  due 
only  to  absorption  by  the  earth  and  straying  due  to  the  spherical  form  of  the 
earth,  without  assuming  any  effect  due  to  ionization  or  heterogeneity  of 
the  atmosphere. 

Particularly  complicated  conditions  occur  at  sunrise  and  sunset. 
They  are  best  illustrated  by  curves  given  by  MARCONI  m  and  reproduced 
in  Fig.  3 18;  the  abscissae  represent  Greenwich  time  in  hours,  the  ordinates 
the  intensity  of  the  signals  received  in  Clifden  (Ireland)  from  Glace  Bay 
(Canada),  drawn  to  a  convenient  scale,  the  full  line  curve  referring  to 
X  =  7000  m.,  the  dotted  curve  toX  =  5000  m.  These  curves  indicate  a 
very  constant  intensity  during  the  day,  but  shortly  after  sunset  in 

*  Nor  have  we  any  explanation  worthy  of  serious  consideration  for  MARCONI'S*  91 
observation  of  the  fact  that  the  bad  effect  of  land  and  mountainous  country  upon 
wave  propagation  with  comparatively  short  waves  exists  in  the  daytime,  but  not 
at  night. 

To  be  sure  it  is  not  clear  whether  MARCONI'S  statements  are  general  or  are  intended 
to  refer  only  to  communication  between  England  and  Mediterranean  points,  in  which 
latter  case  particularly  complicated  conditions  seem  to  be  involved  (see  foot-note  to 
Art.  143o). 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE   267 


Clifden  the  intensity  drops  off,  reaching  a  minimum  about  2  hours 
later.  From  then  on  it  rises  rapidly  to  a  very  high  maximum  occurring 
about  at  the  time  of  sunset  in  Glace  Bay.  Then  the  intensity  gradually 
falls  off  and  during  the  period  when  darkness  covers  the  entire  Atlantic 


Sunset 

Sunset                                Sunrise       Sunrise 

ik 

in                                         in                in 

Clifden 

Glace  Bay                                Clifden     Glace  Bay 

Night  over  the           \ 

L 

\Entire  Atlantic  Ocean;  A 
I      Intensity  Greatly       fl  I 
vl             Variable        •      UrA 

f 

J\ 

1              JLJL 

\ 

7 

I                                                                     '\         X"™ 

V 

// 

\                *^"" 

^  — 

\ 

J  . 

v/. 

12    1     2     3     4     5     6      78 

9    10    11    12  1     234     56     78     9     10  11    12 

loon 

Midnight                                                       Noon 

FIG.  318. 


Ocean,  it  is  extremely  variable.  Shortly  before  sunrise  at  Clifden  the 
signals  again  gradually  increase  in  intensity  until  they  reach  a  maximum 
just  after  sunrise  at  Clifden.  Then  the  intensity  falls  off  again  to  a  de- 


GlaixBay 


Minimum 

FIG.  319. 


Maximum. 

FIG.  320. 


cided  minimum,  which  occurs  an  hour  or  two  before  sunrise  at  Glace  Bay, 
after  which  it  rises  to  the  normal  day  value  again. 

In  Figs.  319-322  the  distribution  of  light  and  darkness  (the  latter 


Maximum, 

FIG.  321. 


Afifuauan 

FIG.  322. 


shaded)  is  sketched  for  the  times  at  which  the  minimum  and  maximum 
intensities  occur.  From  these  it  is  apparent  that  MARCONI'S  observations 
would  find  a  ready  explanation  if  the  waves  in  the  ionized  region  had  a 
lower  velocity  of  propagation  than  those  in  the  unionized  region  and  that, 


268  WIRELESS  TELEGRAPHY 

in  passing  from  the  slightly  to  the  greatly  ionized*  portion  of  the  atmos- 
phere and  vice  versa,  considerable  reflection  f  occurs. 

The  effect  of  the  wave-length  in  this  connection  should  be  noted.  While 
theintensity  of  the  5000  m.  wave  is  considerably  lower  during  the  day  than 
that  of  the  7000  m.  wave,  yet  the  shorter  wave  reaches  a  considerably 
higher  maximum  at  the  points  of  sunrise  and  sunset. 

e.  We  have  proceeded  partly  under  the  assumption  that  observed 
differences  between  night  and  day  transmission  involved  an  indirect 
effect  of  the  daylight,  viz.,  the  light  affected  the  brush  discharge  of  the 
antenna  and  thereby  the  damping  and  amplitude  of  the  oscillations. 

This  might  occur  in  either  of  two  ways.  Thus,  the  photoelectric 
action  of  the  light  upon  the  upper  surface  of  the  antenna  might  increase 
the  discharge  from  the  antenna.  This  is  made  very  improbable  by  the 
fact  that  the  photoelectric  action  of  daylight  at  the  surface  of  the  earth 
upon  impure  metallic  (or  copper)  surfaces  is  very  slight. 

Otherwise  the  daylight,  by  increasing  the  conductivity  of  the  air, 
might  indirectly  affect  the  brush  discharge.  At  points  where  a  brush 
discharge  occurs  at  night,  there  is  probably  no  appreciable  change  during 
the  day,  as  the  effect  of  the  daylight  is  extremely  small  in  comparison 
to  that  of  Jbhe  strong  ionization  caused  by  the  antenna's  electrical  field. 
But  it  is  conceivable  that  at  such  points  of  the  antenna  where  the  poten- 
tial amplitude  is  not  quite  sufficient  to  cause  a  brush  discharge  during  the 
night,  the  additional  direct  or  indirect  effect  of  daylight  might  produce  a 
brush  discharge.  • 

Laboratory  tests242  with  coils  and  simple  aerials  have  shown  no 
appreciable  effect  due  to  strong  ultra-violet  light  ;J  damping  measurements 
on  antennae  in  our  latitude  did  not  give  sufficient  differences  in  the  decre- 
ment between  night  and  day  as  to  explain  the  difference  between  night 
and  day  transmission.243  In  the  tropics,  however,  the  day  values  have  at 
times  been  found  to  be  very  much  higher  than  the  night  values. 

/.  The  following  practical  conclusions  may  be  drawn  from  what  has 
been  stated  in  d  as  to  the  differences  between  day  and  night  transmission : 

*  It  is  here  not  a  question  of  whether  a  portion  of  the  atmosphere  is  light  or  dark, 
as  the  lower  layers  of  the  atmosphere  are  always  to 
be  considered  as  slightly  ionized  whether  in  daylight 
or  not.  Thus  Fig.  320,  if  the  slightly  ionized  region 
were  shaded,  would  appear,  on  a  somewhat  larger 
scale,  as  shown  in  Fig.  323. 
FIG.  323.  t  Perhaps  herein  may  also  be  found  the  explana- 

tion of  MARcoNi's191  observation  that  the  range  at 

night  is  greater  in  a  north-south  or  south-north  direction  than  in  an  east-west  or 
west-east  direction. 

J  MARCONi's239  observation  that  the  effect  of  daylight  upon  transmission  becomes 
noticeable  only  at  relatively  great  distances  (say  over  250  km.),  also  makes  it  very 
improbable  that  light  affects  the  oscillations  of  a  transmitter. 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE  269 

1.  As  waves  of  great  length  are  considerably  more  advantageous  in 
the  daytime,  but  have  no  great  increase  in  their  action  at  night,  while 
shorter  waves,  though  weaker  in  the  daytime,  have  their  radius  of  action 
greatly  increased  at  night,  it  would  appear  advisable  to  operate  with 
relatively  longer  waves  in  the  daytime  and  with  shorter  waves  at  night. 
This,  in  fact,  is  occasionally  done  in  practice. 

2.  It  is  often  stated  as  evidence  of  the  range  of  a  station  that  its  signals 
have  been  clearly  received  at  night  by  some  other  distant  station.     As 
night  transmission  is  always  irregular,  only  the  negative  conclusion  that 
the  two  stations  are  not  capable  of  regular  and  constant  communication 
can  be  drawn  with  safety. 

146.  Actual  Measurements  of  the  Wave  Propagation. — The  theo- 
retical results  of  Art.  138  et  seq.  were  based  upon  the  assumption  of  more  or 
less  ideal  limiting  cases.  It  is  very  important  therefore  to  study  the  results 
of  actual  reliable  tests. 

a.  Only  such  tests  in  which  the  conditions  governing  wave  propaga- 
tion in  wireless  telegraphy  are  duplicated  should  be  considered.     This 
eliminates : 

1.  All  laboratory  tests  or  tests  made  in  the  immediate  vicinity  of 
buildings,  as  reflection  from  the  walls  and  disturbances  due  to  conductors 
are  apt  to  greatly  modify  the  results,  unless  the  work  is  done  with  very 
short  waves  [see  exception  3  in  this  connection]. 

2.  All  tests  in  which  the  distance  between  transmitter  and  receiver 
is  not  considerably  greater  than  one  wave-length.     In  radio-telegraphy 
we  deal  almost  entirely  with  the  field  at  a  great  distance  from  the  trans- 
mitter, which  is  apt  to  be  quite  different  from  the  field  near  the  transmit- 
ter, particularly  as  the  falling  off  in  amplitude  obeys  totally  different 
laws  at  great  distances  than  in  the  proximity  of  the  transmitting  aerial. 

3.  All  tests  in  which  the  wave-length  is  much  different  from  those 
used  in  radio-telegraphy;  according  to  Art.  139,  the  wave-length  is  a  factor 
in  determining  the  form  and  absorption  of  the  waves. 

b.  The   early  experiments   of   W.   DUDDELL   and   J.   E.   TAYLOR228 
have  shown  that  over  sea  the  amplitude — excepting  in  the  immediate 

vicinity  of  the  transmitter — varies  approximately,  as  -.     These   tests 

were  made  over  distances  of  from  16  to  60  miles.     Similar  tests  by  C. 
TissoT228  gave  the  same  results. 

More  recently,  L.  W.  AusTiN244  conducted  very  careful  measure- 
ments involving  very  long  distances  (up  to  1000  nautical  miles),  using  the 
high  power  station  at  Brant  Rock  as  transmitter  and  a  receiver  on  board 
a  U.  S.  battleship.  He  found  that  the  reduction  in  amplitude  is  con- 
siderably more  rapid  than  would  correspond  to  °c  -  and  also  that  it  is  less 
rapid  for  long  than  for  short  waves  in  the  daytime. 


270 


WIRELESS  TELEGRAPHY 


Thus  Fig.  324  represents  the  result  of  a  series  of  observations.  The 
ordinates  are  the  values  of  the  effective  current  in  the  receiver,  which, 
other  things  remaining  equal,  is  proportional  to  the  amplitude  of  the 
electric  field  strength  at  the  receiver.  The  dotted  curve  is  plotted  to 

show  what  occurs  under  the  assumption  —  amplitude  °c  -,  i.e.,  that  there 

is  neither  any  absorption  [Art.  139]  nor  a  stray  field  [Art.  140].     The 
actual  observations  are  plotted  as  small  crosses;*  they  are  all  below  the 

dotted  curve,  the  day  observations 
following  the  full  line  curve  fairly 
closely.  This  curve  is  calculated 
from  an  empirical  equation  which 
seems  to  correspond  quite  well  with 
the  observations,  f  This  equation 
gives  the  value  of  the  effective  cur- 
rent in  the  receiver  as  equal  to 


0.6 


0.5 


0.4 


o* 


AT 


\ 


100 


N: 


N 


200  Naut. 
Miles 


-0.0015 


r\ 


-  -  e 


200       400        600 

FIG.  324. 


800 


1000 
Naut.  Miles 


where   A    is    a   constant,   /«//  the 

°-^ I    I    I    I    ^    I    ^    I    I  effective  current  in  the  transmit- 

ter, hi  and  h%  the  heights  of  the 
transmitting  and  receiving  antennae 
respectively,  all  lengths  being  ex- 
pressed in  kilometers. 

c.  In  regard  to  propagation  over  land,  the  measurements  of  DTJDDELL, 
and  TAYLOR228  already  showed  that  at  considerable  distances  from  the 

transmitter  the  amplitude  falls  off  more  rapidly  than  the  factor  — 

L.  W.  AusTiN245in  tests  over  45  miles  of  land  found  that  the  absorption 
with  X  =  3750  m.,  was  hardly  greater  than  over  sea,  but  that  with  X  = 
1000  m.  it  was  much  greater  over  land. 

It  seems  evident  from  a  great  number  of  observations  that  the  reduc- 
tion in  amplitude  is  largely  dependent  upon  the  nature  of  the  ground 
involved,  whether  it  is  the  different  petrologic  formations  or  differences 
in  the  moisture  contained  which  are  the  determining  factors,  and  that  in 
general  much  moisture  is  favorable,  dryness  unfavorable  to  the  wave 
propagation. 

147.  Effect  of  Grounding  the  Transmitter  upon  the  Wave  Propagation. — 

*  The  crosses  within  a  circle  represent  observations  with  a  galvanometer  and 
detector,  the  plain  crosses  those  made  with  a  telephone  and  detector  [Art.  51].  The 
letter  N  over  a  cross  indicates  a  night  observation. 

t  hi  and  A2  were  varied  from  12  to  43  m.,  /„//  from  7  to  30  amp.,  X  from  300  to 
3750  m.,  r  from  30  to  1000  nautical  miles. 


PROPAGATION  OF  THE  WAVES  OVER  THE  EARTH'S  SURFACE   271 

A  study  of  the  effect  of  grounding  in  radio-telegraphy  must  be  subdivided 
under  the  following  two  questions: 

1.  What  is  the  effect  upon  the  oscillations   (their  frequency,   distri- 
bution and  amplitude  of  the  current,  damping)? 

2.  What  is  the  effect  upon  the  propagation  of  the  waves? 

The  first  question  was  discussed  in  Art.  99  et  seq.,  the  second  in  Art. 
138  et  seq.  From  these,  however,  a  third  question  suggests  itself,  viz., 
have  the  extent  and  manner  of  grounding  the  transmitting  antenna  any 
effect  upon  the  propagation  of  the  waves? 

With  sea  water  such  an  effect  would  seem  a  priori  very  improbable ; 
not  so  however  with  dry  land.  Certainly  it  is  conceivable  that  extending 
or  not  extending  the  ground  connection  to  the  ground  water  would  have 
a  different  effect  not  merely  upon  the  ground  resistance,  but  also  upon  the 
propagation  of  the  waves. 

If  it  is  desired  to  answer  this  question  with  actual  tests,*  it  is  abso- 
lutely essential  to  prevent  changes  in  the  ground  connection  from  affecting 
the  antenna  oscillations,  i.e.,  the  frequency,  damping,  current  amplitude 
and  distribution  must  remain  constant.  Otherwise  the  tests  will  give 
no  information.  It  is  very  doubtful  that  any  reliable  tests  in  which  all 
such  influences  were  entirely  eliminated  have  ever  been  recorded. 

148.  The  Safety  Factor.— From  Arts.  142  and  144  et  seq.,  it  follows 
that  the  effect  of  a  given  transmitter  upon  a  given  receiver  is  influenced 
by  various  conditions,  such  as  weather  conditions.  Hence,  where  it  is 
required  that  communication  between  the  given  stations  shall  not  simply 
stop  whenever  a  combination  of  unfavorable  conditions  arises,  it  is  neces- 
sary to  introduce  a  considerable  "factor  of  safety."  The  "range"  of 
the  transmitter,  i.e.,  the  distance  at  which  the  receiver  is  still  just 
able  to  distinctly  receive  the  signals,  must  be  considerably  greater  than 
the  distance  between  the  two  stations  for  maintaining  uninterrupted 
communication. 

The  TELEFUNKEN  Co.  formerly  used  a  safety  factor  of  3,246  i.e.,  the 
range  of  its  commercial  stations  had  to  be  three  times  as  great  as  the  dis- 
tance to  be  bridged  in  regular  service. 

*  The  literature  of  radio-telegraphy  abounds  with  such  tests. 


CHAPTER  XI 


DETECTORS 


247 


No  direct  detection  of  the  electromagnetic  waves  emanating  from  a 
radio-transmitter  is  possible.  We  are  limited  to  causing  the  waves  to 
induce  oscillations  in  the  conductors  of  the  receiver  and  to  detect  these 
oscillations  by  means  of  suitable  apparatus.  Hence  the  names  "wave 
indicators/'  "detectors,"  etc.,  although  these  devices  really  indicate  the 
oscillations  in  the  circuits  in  which  they  are  connected. 

1.  THERMAL  DETECTORS 

149.  Bolometer  and  Thermogalvanometer. — The  currents  induced 
in  radio-receivers,  as  soon  as  distances  of  any  great  extent  are  involved, 
are  of  very  low  amplitude.  Hence  if  the  heat  developed  by  these  currents 
is  to  be  used  for  their  detection,  only  the  more  sensi- 
tive of  the  apparatus  already  described  [Art.  4  et 
seq.],  such  as  the  bolometer,  thermocouple  and 
thermal  galvanometer  can  come  into  consideration, 
and  even  then  only  for  moderate  distances. 

The  bolometer  has  been  extensively  used  by  C. 
TissoT248  and  others  for  radio-measurements.  Its 
form  was,  in  principle,  that  shown  in  Fig.  102,  the 
bolometer  wire  being  very  fine  and  enclosed  in  a 
vacuum  tube.  Later  the  bridge  connection  was 
replaced  by  the  compensation  method  of  connection 
devised  by  BELA  GATI. 

The  wave  indicator  used  by  R.  FESSENDEK  and 
others  under  the  name  of  "  solid  barretter,"  consists 
essentially  of  a  very  fine  platinum  wire  (so-called 
Wollaston  wire)  (P  in  Fig.  325)  of  0.002  mm.  diameter  and  0.4  mm. 
long  in  a  glass  vessel  (G,  Fig.  325)  containing  a  vacuum.  To  prevent 
a  loss  of  heat  by  radiation,  the  wire  is  enclosed  in  a  small  container,  S, 
of  silvered  glass.  FESSENDEN  did  not,  at  least  not  in  all  cases,  use  this 
barretter  in  connection  with  a  bridge,  but  placed  it  directly  in  a  telephone 
circuit,  so  that  the  telephone  responded  to  the  current  variations  caused 
by  the  changes  in  the  resistance  of  the  wire. 

The  thermal  galvanometer  has  proven  itself  well  suited  to  measure- 
ments at  moderate  distances,  and  was  used  among  others  by  W.  DUDDELL 

272 


FIG.  325. 


DETECTORS  273 

and  J.  E.  TAYLOR228  and  also  by  MARCONI249  in  his  experiments  with 
directional  telegraphy. 

150.  Thermocouples. — Thermal  Detectors. — The  wave  indicators 
whose  action  depends  upon  thermoelectric  effects  may  be  divided  into 
three  classes,  as  follows: 

a.  Thermocouples  of  wires  [Art.  48].  Excellent  as  these  are  for 
laboratory  purposes,  they  are  hardly  sensitive  enough  for  general  use  as 
wave  indicators,  in  spite  of  all  precautions  to  minimize  heat  losses  and 
the  use  of  very  short  and  thin  wires. 

6.  Thermal  Detectors  with  Point  Contacts*™ — The  requirement  for 
maximum  sensitiveness  in  a  thermocouple  (thermal  detector)  would  ap- 
pear to  be  the  production  of  the  greatest 
temperature  rise  at  the  point  of  contact. 
Hence  it  is  important  that  those  parts  of  the 
thermocouple  in  which  the  heat  is  developed, 
aside  from  having  the  lowest  possible  specific 
heat,  have  as  small  a  mass  and  surface  as 
possible.  With  thermocouples  made  of  wire 
this  is  obtained  by  the  use  of  very  fine  wires  .„ 

(and  the   minimum  of  solder,  where  this  is 

used).     But  another  method  is  to  have  one   of   the   elements  of  the 
thermocouple  touch  the  other  at  a  point  or  knife-edge. 

Thermal  detectors  of  this  type  have  been  devised  of  numberless  com- 
binations, such  as  tellurium-aluminium  (L.  W.  AUSTIN,  NAT.  ELEC. 
SIG.  Co.),  tellurium-galena  (C.  LORENZ),  silicon-copper  (G.  H.  PICKARD), 
tinfoil-galena  (TELEFUNKEN  Co.)  and  also  the  extensively  used  graphite- 
galena  combination.* 

The  usual  arrangement  is  to  have  one  of  the  elements  pressed  against 
the  other  by  means  of  a  spring  and  to  provide  a  fine  adjustment  for  regu- 
lating the  pressure. 

In  some  forms  one  metal  is  disc-shaped  and  kept  in  constant  rotation 
while  the  other  brushes  over  it  with  a  slight  pressure  (L.  W.  AUSTIN). 

c.  Thermal  Detectors  with  Heating  Device,  f — An  example  of  this  type 
is  found  in  W.  SCHLOMILCH'S  (TELEFUNKEN  Co.)  thermal  detector.  In 
this,  one  element  is  a  platinum  wire  with  a  small  bend  in  it  (A,  Fig.  326), 
pressing  lightly  against  a  disc  of  oxidized  copper.  The  platinum  wire 
is  heated  by  means  of  a  small  alcohol  flame,  so  that  a  thermoelectric 
force  exists  at  all  times;  the  oscillations  therefore  simply  vary,  rather 
than  create  the  thermoelectric  force.  This  detector  is  no  longer  used  in 
practice. 


*  With  some  of  these  detectors,  however,  it  is  not  certain  that  the  action  is  really 
thermoelectric  [Art.  160c]. 

t  See  Art.  162a  regarding  the  purpose  of  this  heating  device. 
18 


274  WIRELESS  TELEGRAPHY 

151.  Relative  Importance  of  the  Thermal  Detectors. — Most  of  the 
thermal  wave  indicators  mentioned  in  what  has  preceded  are  preemi- 
nently adapted  for  certain  quantitative  determinations  in  radio-telegraphy. 
For  some  of  these  measurements,  transmitter  and  receiver  need  only  be 
separated  by  a  few  kilometers.     But  even  where  a  distance  of  several 
hundred  kilometers  is  necessary,  some  of  the  thermal  detectors  have 
sufficient  sensitiveness  to  serve  the  purpose,  and  in  comparison  to  other 
wave  indicators  they  have  the  great  advantage  that  their  deflection  is 
due  exclusively  to  the  current  effect,  even  though  not  necessarily  propor- 
tional to  it. 

This  property  of  the  thermal  detectors,  however,  is  not  without  its 
danger.  For  it  is  conceivable  that  results  obtained  with  the  thermal 
indicators  are  applied  to  methods  using  other  wave  detectors  without 
consideration  of  the  question  whether  the  latter  also  respond  to  the  current 
effect. 

2.  MAGNETIC  DETECTORS251 

152.  The   Fundamental   Physical   Principles. — Assume   a   magnetic 
field  M  induced  by  means  of  a  permanent  or  electromagnet  in  some  steel 
or  hard  drawn  iron  wires.     If,  then,  these  wires  are  subjected  to  the  field 
of  an  electromagnetic  oscillation,  e.g.,  that  produced  by  the  discharge 
of  a  condenser  circuit,  the  result  will  be  a  change  in  the  magnetic  flux  in 
the  wires.     We  may  state  therefore :  The  result  of  the  action  of  the  oscilla- 
tions— no  matter  through  what  processes  it  is  obtained251 — is  a  very  rapid 
change  in  the  magnetic  flux  in  the  wires. 

If  the  same  thing  is  repeated  with  the  same  wires,  the  effect  is  only 
very  slight.  If  it  is  desired  that  a  second  discharge  again  have  a  material 
effect  upon  the  magnetic  flux  in  the  wires,  it  is  necessary  to  alter  the  mag- 
netic field  M  between  the  first  and  second  discharges,  as,  e.g.,  by  increas- 
ing or  decreasing  the  current  in  the  electromagnet,  or,  if  a  permanent 
magnet  is  used,  by  altering  its  distance  from  the  wires. 

Hence,  if  iron  or  steel  is  to  be  used  as  an  indicator  of  electromagnetic 
waves  and  is  to  react  upon  any  sequence  of  these,  it  is  absolutely  essential 
that  the  external  field  is  continuously  varied,252  or  that  new  iron  parts  are 
constantly  subjected  to  the  action  of  the  electromagnetic  oscillations. 

153.  Marconi's  Magnetic  Detector. — MARCONI,  probably  following  up 
the  work  of  RUTHERFORD,  used  two  different  forms. 

a.  The  first  is  shown  diagrammatically  in  its  essentials  in  Fig.  327.  A 
bundle  of  hard-drawn  iron  wires  is  enclosed  within  the  winding,  S\, 
through  which  the  oscillations  of  the  receiver  pass.  The  variable  mag- 
netic field,  M ,  is  obtained  by  rotation  of  the  horseshoe  magnet,  H,  fast- 
ened to  the  axle,  A.  The  rapid  change  in  the  magnetic  flux  in  the  iron 
wires  caused  by  the  oscillations,  induces  an  e.m.f.  in  the  winding,  >S2. 


DETECTORS 


275 


This  produces  a  clicking  sound  in  the  telephone,  T,  connected  in  circuit 
with  $2,  every  time  an  electromagnetic  wave  strikes  the  receiver. 

6.  In  practice  MARCONI  seems  to  have  used  only  his  second  method, 
which  is  shown  diagrammatically  in  Fig.  328.  The  iron  wires  are  formed 
into  an  endless  string  or  rope,  D,  running  over  two  grooved  pulleys  and 
kept  in  motion  by  a  clockwork.  The  magnetic  field,  M,  in  the  iron  wires, 
is  induced  by  two  horseshoe  magnets,  H,  under  whose  poles  the  wires  are 
passed. 

When  the  wires  pass  through  the  inside  of  the  winding,  Si,  which  is 
connected  into  the  receiving  circuit,  they  are  subjected  to  the  action  of 


the  oscillations.  The  latter  are  here  also  indicated  by  means  of  a  tele- 
phone connected  to  the  coil  S2. 

MARCONI  succeeded  in  operating  a  relay  with  this  detector  [Art.  167c] 
and  thereby  to  automatically  record  the  received  messages,253  but  at 
present  he  seems  to  prefer  the  use  of  a  suspension  galvanometer  [Art. 
1676]  for  recording  telegrams. 

154.  Other  Forms  of  Magnetic  Detectors. — In  another  class  of  mag- 
netic wave  indicators,  the  iron  body  subjected  to  the  action  of  the  re- 
ceived oscillations,  is  located  in  a  rotating  magnetic  field,  or  is  itself  ro- 
tated in  a  fixed  constant  field.  To  this  class  belong  the  arrangements254 
of  R.  ARNO,  J.  A.  EWING  and  L.  H.  WALTER,  A.  S.  Rossi,  R.  A.  FESSEN- 
DEN,  W.  PEUCKERT  and  another  of  L.  H.  WALTER. 


276 


WIRELESS  TELEGRAPHY 


None  of  these  arrangements  seem  to  have  entered  into  radio-prac- 
tice, for  which  they  are  hardly  so  much  intended  as  for  measuring  purposes. 
For  measurements,  certain  of  these  devices  have  the  advantage  that  their 
action  is  not  determined  by  a  single  oscillation  (as  is  the  case  with 
MARCONI'S  magnetic  wave  indicators)  but  the  effect  of  a  sequence  of  wave 
trains  is  summed  up  to  a  certain  extent,  as  with  the  thermal  detectors. 


3.  IMPERFECT  CONTACTS 

155.  Metallic  Granular  Coherer.255 — In  its  original  form  the 
"coherer"  consists  of  a  tube  of  non-conducting  material  (e.g.,  a  glass  tube) 
with  two  metallic  electrodes,  EI  and  E2  (Fig.  329),  between  which  are  a 
large  number  of  very  small  pieces  of  some  suitable  metal  (granules, 


shavings).  This  in  its  normal  condition  offers  an  almost  infinite  resist- 
ance. If,  however,  sufficiently  strong  oscillations  are  passed  through  this 
coherer,  its  resistance  is  greatly  decreased,  falling  to  several  thousand  or, 
in  some  coherers,  even  to  a  few  hundred  ohms  or  less.  This  low  resist- 
ance is  retained  by  the  coherer  after  the  oscillations  have  ceased.  In 
order  to  bring  it  back  to  its  non-conducting  state,  it  is  necessary  to  shake 
it,  say,  by  tapping  against  the  containing  tube. 


DETECTORS 


277 


Since  the  time  when  BRANLEY  showed  that  this  simple  device  con- 
stituted a  wave  indicator  of  much  higher  sensitiveness  than  the  other  forms 
then  known,  the  coherer  was  improved  and  developed  along  the  following 
lines. 

a.  The  shape  of  the  coherer  was  not  changed  much.  MARCONI  cut 
the  electrode  surfaces  at  an  angle  to  the  axis  (Fig.  330)  so  that  the  space 


between  them  is  wedge-shaped.  In  this  way,  upon  tapping  against  the 
side  of  the  tube  where  the  electrodes  are  closest  together,  there  is  no 
danger  of  jamming  the  metal  filings  between  the  electrodes. 

6.  As  to  the  material,  very  little  of  a  general  nature  can  be  stated. 
MARCONI  used  silver  electrodes  in  his  early  work,  as  it  was  easy  to  form 
an  amalgam  with  the  silver,  and  his  filling  was  a  mixture  of  96  per  cent, 
nickel  and  4  per  cent,  silver.  Similar  coherers  were  long  used  by  the 
TELEFUNKEN  Co.  (Fig.  331).  Later  SCHLOMILCH,  of  the  TELEFUNKEN 
Co.,  devised  a  very  sensitive  coherer  of  gold  and  aluminium;  one  electrode 
being  of  aluminium,  the  other  of  gold,  while  the  filling  is  gold  powder. 


FIG.  331. 

A.  KOEPSEL  obtained  a  very  reliable  coherer  by  using  highly  polished  and 
very  hard  steel  plate  electrodes  and  granules  of  glass-hard  steeL 

In  regard  to  the  filling,  the  chemical  constituency  is  by  no  means  the 
only  determining  factor,  and  the  shape  of  the  granules  is  of  at  least 
equal  importance.  In  general,  high  sensitiveness  is  secured  by  giving 
the  granules  sharp  points  or  edges.  The  danger  of  jamming  with  such 
granules  is  minimized  by  eliminating  all  those  having  a  long  narrow  shape. 

c.  Coherers  are  frequently  exhausted  (vacuum),  this  practice  having 
been  originated  by  MARCONI.  Complete  dryness  inside  the  coherer  is 
assured  in 'this  way — a  requirement  for  reliable  operation. 


278 


WIRELESS  TELEGRAPHY 


d.  Some  coherers  are  arranged  with  adjustable  sensitiveness.  Where 
the  space  containing  the  metal  filings  or  granules  is  decidedly  wedge- 
shaped,  as  in  some  of  the  coherers  formerly  used  by  the  TELEFUNKEN  Co., 
this  adjustment  is  attained  by  simply  turning  the  coherer,  the  sensitive- 
ness being  greater  when  the  narrow  portion  of  the  wedge-shaped  space 
points  downward.  In  other  coherers  the  distance  between  the  electrodes 
is  adjustable,  as  in  those  of  A.  KOEPSEL,  also  in  those  of  H.  BOAS  (Fig. 
332)  *  which  latter  are  in  a  vacuum.  Regulation  of  the  electrodes  through 


FIG.  332. 

the  air-tight  ends  is  made  possible  by  a  flexible  metal  diaphragmf  which 
closes  the  tube  at  one  end  and  against  which  one  of  the  electrodes  is 
pressed  from  within  by  means  of  a  spring.  If,  then,  the  micrometer 
screw  is  turned  from  the  outside,  this  .brings  pressure  against  the  dia- 
phragm, thereby  moving  one  of  the  electrodes  within  certain  limits. 

156.  Mercury  Coherers. — a.  In  some  experiments  of  the  Italian  Navy, 
the  coherer J  shown  diagrammatically  in  Fig.  333,  was  tested.  Two 
electrodes,  either  both  of  iron  or  one  of  iron  and  one 
of  carbon,  are  placed  in  a  glass  tube,  and  between 
the  electrodes  is  a  drop  of  mercury. 

This  coherer,  which  was  also  used  by  MARCONI 
for  a  time  in  some  of  his  long  distance  work,  seems 
to  be  more  sensitive  than  those  having  solid  metal 


nr> 


FIG.  333. 


granules.  Moreover,  it  differs  from  these  in  that  after  the  oscillations 
have  ceased,  it  automatically  returns  to  its  initial  high  resistance.! 
This  form  of  coherer  is  no  longer  used  in  practice,  however. 

b.  Another  form  of  mercury  coherer  has  been  devised,  apparently  inde- 
pendently by  A.  KOEPSEL  on  the  one  hand  and  by  O.  LODGE  and  A. 
MUIRHEAD  on  the  other  hand.256  The  construction  adopted  by  the 
latter  is  shown  diagrammatically  in  Fig.  334.  A  small  steel  wheel,  R,  to 
which  current  is  brought  through  the  brush,  B,  is  rotated  by  clockwork 

*  From  a  pamphlet  of  H.  BOAS. 

t  The  metal  diaphragm  is  soldered  to  a  metal  tube  which,  in  turn,  is  soldered  to 
the  platinum  coating  on  the  glass. 

J  Apparently  the  idea  originated  with  an  Italian  Signal  Officer  name.d  CASTELLI. 
§  It  is  "self-restoring." 


DETECTORS  279 

or  by  a  small  motor.  The  wheel  dips  slightly  into  mercury,  Q,  which  is 
covered  by  a  thin  layer  of  mineral  oil.  Normally  the  wheel  and  mercury 
do  not  make  a  conducting  contact;  a  contact  is  formed,  however,  as  soon 
as  oscillations  pass  through  this  coherer  and  disappears  again  as  soon  as 
the  oscillations  cease. 

These  coherers  of  LODGE  and  MTJIRHEAD  seem  to  have  given  good 
service  in  practice. 

According  to  the  investigations  of  W.  H.  ECCLES,  the  action  of  this 
detector,  as  well  as  of  that  described  in  a,  seems  to  depend  upon  the  nega- 
tive temperature  coefficient  of  the  iron  oxide  coating  which 
forms  on  the  iron  or  steel  electrode.  If  the  oxide  at  the 
point  of  contact  becomes  heated  by  the  oscillations,  its 
resistance  is  greatly  decreased  and  the  current  from  the 
battery  supplying  the  detector  circuit  (see  Fig.  329)  rises 
considerably  above  its  initial  value.  FlG- 

c.  L.  H.  WALTER257  devised  a  very  useful  and  also  self-restoring  mer- 
cury coherer,  the  sensitive  contact  being  made  between  a  tantalum  point 
(T,  Fig.  335)  and  mercury  (M).  This  detector  is  said  to  be  not  quite  so 
sensitive  as,  e.g.,  the  electrolytic,  with  very  weak  oscillations,  but  with 
strong  oscillations  it  gives  much  louder  sounds  in  the  telephone. 

157.  Carbon  or  Graphite  Coherers  (Microphone  Contact). — Another 
class  of  coherers  makes  use  of  carbon  or  graphite.     Two  arc-lamp  car- 
bons, one  resting  loosely  upon  the  other,  or  either  an  arc-lamp  carbon  or  a 
graphite  rod  together  with  a  wire  constitute  the  simplest,  though  im- 
practical forms  of  this  type  of  coherer.     They  suffice  for  the  detection  of 
electromagnetic  oscillations  as  well  as  any  microphone,  which  latter  in  fact 
was  used  by  HUGHES  for  this  purpose  as  far  back  as  1879.     These  coherers, 
like  those  made  of  metal  granules,  change  their  resistance  when  oscilla- 
tions are  passed  through  them,  but  differ  from  them,  resembling  the 
mercury  coherers  in  this  respect,  in  that  they  are  self-restoring. 

This  coherer  was  used  in  practice  for  quite  some  time  in  the  form,  de- 
vised by  A.  KOEPSEL,  in  which  the  imperfect  contact  consisted  of  a  highly 
polished,  very  hard  steel  plate  and  a  hard  graphite  rod.  This  combination 
is  very  sensitive  but  is  not  sufficiently  reliable  for  regular  practice. 

4.  ELECTROLYTIC  AND  OTHER  DETECTORS 

158.  Anti-coherers. — This  name  is  frequently  applied  to  those  de- 
tectors in  which  the  effect  of  the  electromagnetic  oscillations,  instead  of 
being  a  reduction  is  an  increase  in  the  resistance;  these  anti-coherers  more- 
over are  self-restoring. 

a.  De  Forest's  "Responder." — In  a  tube  of  non-conducting  material 
there  are,  as  in  the  ordinary  coherer,  two  metallic  electrodes,  which  some- 
times are  hollowed  out  as  shown  in  Fig.  336.  The  space  between  them  is 


280 


WIRELESS  TELEGRAPHY 


filled  with  a  paste  which  in  one  case,  e.g.,  consists  of  water  and  glycerine, 
metal  filings  and  pulverized  lead. 

DE  FOREST  gives  the  following  explanation  of  its  action.  If  this  de- 
tector is  placed  in  a  battery  circuit,  a  small  current  flows  through  it. 
The  resulting  electrolysis,  causes  the  formation  of 
very  fine  metallic  bridges  between  the  metal 
filings.  The  effect  of  the  oscillations  is  to  destroy 
these  bridges.  When  they  cease,  however,  the 
current  immediately  causes  the  bridges  to  form 
again  so  that  the  wave  indicator  resumes  its  nor- 
mal resistance. 

b.  The  detector  of  J.  E.  IvES258  contains  two 
crossed  silver  wires,  which  almost  make  contact  in 
a  solution  of  potassium  bromide  or  iodide  or  of 
both.     Here  the  formation  of  the  bridges  between 
the  two  wires  has  been  observed  under  the  microscope. 

159.  The  Electrolytic  Detectors  of  Ferrie,  Fessenden,  Nernst  and 
Schlomilch. — It  seems  that  the  electrolytic  detector,  to  be  described  in 
what  follows,  was  announced  independently  by  FERRIE,  R.  FESSENDEN, 
NERNST  and  W.  SCHLOMILCH  after  M.  I.  PUPIN,  at  a  much  earlier  date 
(U.  S.  Patent,  713045,  1898)  had  used  a  similar  cell  for  rectifying  alter- 
nating currents.  The  following  is  a  description  of  the  form  in  which  the 
electrolytic  detector  was  used  by  the  TELEFUNKEN  Co.,  under  the  name 
of  "SCHLOMILCH  cell"  (Fig.  337): 


FIG.  336. 


FIG.  337. 


FIG.  338. 


In  a  container  filled  with  dilute  sulphuric  acid  there  are  two  platinum 
wire  electrodes,  one  of  which  is  very  thin  and  covered  by  glass  tubing, 
except  at  its  end  where  the  bare  wire  projects  for  a  very  short  distance. 
This  thin  wire  is  connected  to  the  positive  pole,  the  heavier  wire  to  the 
negative  pole  of  a  battery  whose  e.m.f.  is  only  slightly  greater  than  the 
e.m.f.  which  is  produced  by  the  polarization  of  the  cell,  platinum — dilute 
sulphuric  acid — platinum.  Consequently  a  very  small  current  flows 
through  the  cell,  so  that  a  galvanometer  connected  in  circuit  would  show  a 


DETECTORS 


281 


slight  deflection.  As  soon  as  oscillations  act  upon  the  detector,  a  consid- 
erable increase  in  the  current  results,  so  that  the  galvanometer  in  the  cell 
circuit  has  a  much  greater  deflection  and  a  clicking  sound  is  heard  in  a 
telephone  connected  in  the  circuit.  The  moment  the  oscillations  cease, 
the  current  falls  to  its  normal  value.  Fig.  338*  is  an  exterior  view  of  the 
detector. 

In  FsssENDEN's259  "liquid  barretter"  (Fig.  339)  the  point  of  a  fine 
Wollaston  wire  (platinum  wire  coated  with  silver)  just  dips  into  the  sur- 
face of  the  electrolyte  (potassium  nitrate  solution)  ;f  here  also  the  Wol- 
laston wire  is  joined  to  the  posi- 
tive pole.  A  very  fine  adjust- 
ment makes  it  possible  to  secure 
the  most  efficient  depth  of  sub- 
mersion and  also  enables  prompt 
readjustment  in  case  the  point 
of  the  wire  is  harmed  at  any 
time  by  too  heavy  a  discharge. 

a.  The  characteristic  prop- 
erties of  the  electrolytic  de- 
tector are: 

1.  The  sensitiveness  increases 
as  the  surface  area  of  the  posi- 
tive electrode  decreases.    Hence, 
an  extremely  small  electrode  is 
used  for  radio-purposes.    In  the 

SCHLOMILCH  detector  it  is  a  platinum  wire  of  about  0.03  mm.  diameter, 
in  glass,  from  which  it  projects  only  very  slightly,  while  in  FESSENDEN'S 
liquid  barretter  it  is  a  Wollaston  wire  of  still  much -smaller  diameter. 

2.  The  normal  resistance  of  the  cell,  when  not  excited  by  oscillations  is 
only  several  thousand  ohms,  hence  is  of  about  the  same  order  as  that  of 
the  coherer  when  excited. 

3.  Other  things  being  equalf  the  galvanometer  deflection  or  the  inten- 
sity .of  the  sound  in  the  telephone  increases  as  the  amplitude  of  the  oscil- 
lations is  increased.261 

The  investigations  of  G.  W.  PiERCE1  (which,  however,  were  made  with 
low  frequency  alternating  current)  indicate  that  the  electrolytic  detector 

*  From  a  pamphlet  of  the  TELEFUNKEN  Co.  In  this  form  the  positive  electrode  is 
renewable.  A  later  construction  of  the  TELEFUNKEN  Go's,  electrolytic  detector  has 
three  fine  wire  electrodes,  which  can  be  used  alternately.260 

t  According  to  J.  E.  IvEs259  a  solution  of  caustic  potash  (1  vol.  saturated  solution 
to  2  vols.  water)  increases  the  resistance  of  the  detector,  but  also  increases  the  range 
of  its  variation  due  to  the  oscillations.  IVES  used  a  Wollaston  wire  of  0.001  mm. 
diameter  (of  the  platinum),  submerged  to  a  depth  of  about  0.1  mm. 

t  That  is,  with  constant  decrement,  as  this  determines  the  galvanometer  deflection 
as  well  as  the  amplitude  of  the  oscillations. 


FIG.  339. 


282  WIRELESS  TELEGRAPHY 

acts  as  a  rectifier  due  to  the  polarization  [see  Art.  162a],the  resultant  cur- 
rent being  unidirectional. 

b.  FESSENDEN262  found  that  with  his  liquid  barretter  the  signals  in  the 
telephone  became  louder  and  sharper  on  applying  a  pressure  of  three  to 
four  atmospheres  to  the  barretter. 

c.  The  customary  method  is  to  connect  the  electrolytic  detector  in 
series  with  a  battery  and  a  telephone.     It  has  often  been  proposed  to  elim- 
inate the  battery,  by  using  for  the  non-sensitive  electrode  of  the  detector, 
a  metal  which,  together  with  the  sensitive  electrode,  will  form  a  galvanic 
cell  of  suitable  e.m.f. 

160.  Crystal  Detectors. — There  are  a  number  of  crystalline  substances 
which,  when  substituted  for  the  coherer  in  the  arrangement  of  Fig.  329, 
produce  a  galvanometer  deflection  or  sound  in  the  telephone,  whenever 
oscillations  are  passed  through  the  circuit.  All  these  substances  can, 
therefore,  be  used  as  wave  indicators. 

a.  The  use  of  these  substances  as  wave  indicators  probably  originated 
with  the  experiments  of  F.  BRATJN  (1901) 263  in  connection  with  psilo- 
melan  (a  complex  mineral  of  irregular  composition  and  containing  man- 
ganin),  also  with  galena  (PbS),iron  pyrites  (FeS2)  and  pyrolusite  (MnO2). 
At  the  suggestion  of  BRAUN,  the  TELEFUNKEN  Co.  developed  the  psilo- 
melan  detector;  its  sensitiveness  was  brought  to  a  degree  about  equal  to 
that  of  the  SCHLOMILCH  electrolytic  detector. 

The  following  substances  have  since  then  been  proposed  and  widely 
used  in  practice:263  carborundum  (SiC)  (DUNWOODY),  titanium  di- 
oxide (Ti02),  molybdenite  (MoS2)  (G.  W.  PIERCE),  copper  pyrites 
(CuFeS2),  also  (Cu3FeS3),  chalcocite  (Cu2S),  manganese  dioxide  (MnO2) , 
and  iron  pyrites  (FeS2). 

The  usual  method  is  to  place  a  small  piece  of  one  of  these  minerals  be- 
tween two  metal  electrodes  (of  almost  any  suitable  material)  under  light 
pressure,  and  in  series  with  a  battery  and  telephone  in  the  circuit  receiving 
the  oscillations.  The  use  of  a  plate  of  the  detector  material  in  conjunc- 
tion with  a  metallic  powder  (thus,  molybdenite — powdered  silver)  has 
also  been  proposed. 

In  this  same  class  also  belongs  the  detector  of  S.  G.  BROWN,  in  which 
lead  peroxide  is  placed  between  a  lead  and  a  platinum  electrode,  the  lead 
being  connected  to  the  negative,  the  platinum  to  the  positive  pole  of 
the  battery. 

b.  In  a  second  class  of  detectors  either  a  combination  of  two  minerals 
or  of  one  mineral  with  some  specific  metal  is  used.     To  this  class  belongs, 
e.g.,  the  "perikon"  detector  of  G.  J.  PicKARD,263  which  is  a  combination  of 
zinc  oxide  (ZnO)  and  copper  pyrites  (CuFeS2). 

c.  As  to  the  nature  of  the  action  of  these  detectors,264"  it  suggests  itself 
that  this  may  be  thermoelectric.     In  fact  C.  TISSOT  has  shown  that  this 
is  very  probably  the  case  with  a  number  of  detectors — the  combinations 


DETECTORS  283 

metal-copper  pyrites,  metal-chalcocite,  metal-manganese  dioxide,  metal- 
tellurium.     He  proved  that: 

1.  These  detectors  are  sensitive  only  if  the  contact  is  limited  to  a 
point. 

2.  They  operate  without  a  battery  in  series,  and  when  a  battery  is 
used  the  sensitiveness  does  not  depend  upon  the  value  or  direction  of  its 
e.m.f. 

3.  The  direction  of  the  current  (direct)  obtained  under  the  influence 
of  the  received  oscillations  is  always  the  same  as  'the  direction  of  the 
therrno-e.m.f. 

With  another  group,  however — carborundum,  anatase  (titanium  diox- 
ide), molybdenite  and  the  perikon  detector — TISSOT'S  tests  established 
that: 

1.  The  form  of  the  contact  is  of  little  or  no  importance,  even  relatively 
large    polished    plates   placed   between    two   metallic   electrodes  make 
sensitive  detectors. 

2.  The  use  of  a  battery  in  series  with  the  detector,  with  proper  value 
and  direction  of  the  battery  e.m.f.,  increases  the  sensitiveness. 

3.  The  sensitiveness  of  these  detectors  bears  no  relation  whatever 
to  the  value  of  their  thermo-e.m.f. 

He,  therefore,  concludes  that  in  this  last  mentioned  group  thermo- 
electric forces  play  no  important  part  in  their  action  as  detectors. 

G.  W.  PIERCE,  l  as  the  result  of  extensive  investigations,  including 
oscillograph  records  made  with  the  BRATTN  tube,  concluded  that  with 
carborundum,  anatase,  brookite  (another  form  of  TiO2)  and  silicon,  ther- 
moelectric forces  were  not  involved,  but  that  these  detectors  were  better 
conductors  in  one  direction  than  in  the  other,  in  short,  act  as  rectifiers 
[Art.  162]. 

161.  Incandescent  Lamp  Detectors,  Gas  Detectors. — a.  J.  A.  FLEM- 
ING265 observed  the  following  phenomenon:  An  electrode  (A,  Fig.  340), 
say  of  cylindrical  form,  is  fused  into  an  incandescent  lamp  bulb,  whose 
filament  is  made  incandescent^  by  means  of  a  battery,  B.*  A  circuit 
containing  a  galvanometer,  G,  (or  telephone) and  a  coil,$2,  is  joined  to  the 
electrode,  A,  at  one  end  and  to  the  lamp  filament,  at  the  other,  K.  The 
aerial  coil  Si  is  coupled  with  /S2;  hence  if  oscillations  pass  through  $1,  the 
oscillations  induced  in  the  circuit  AGS^K  will  cause  the  galvanometer 
to  deflect  (or  produce  a  sound  in  the  telephone).  The  galvanometer 
needle  will  return  to  its  zero  position  as  soon  as  the  oscillations  cease, 
i.e.,  the  arrangement  is  a  self-restoring  wave  indicator. 

Several  years  ago  C.  TissoT265  used  this  wave  indicator  for  measure- 
ments over  considerably  long  ranges  but  he  complains  of  the  irregularity 

*  A  choke  coil  [Art.  1656]  should  be  inserted  in  the  leads  from  the  battery  to  the 
lamp. 


284 


WIRELESS  TELEGRAPHY 


of  the  deflections.*  But  in  the  more  recent  form  of  FLEMING'S  " oscilla- 
tion- valve,"  the  anode  being  a  cylinder  of  carbon  and  the  cathode  a 
tungsten  wire,  this  detector  seems  to  have  met  all  reasonable  require- 
ments as  to  sensitiveness  and  reliability.  This  is  borne  out  by  the  fact 
that  MARCONI  has  been  using  it,  in  conjunction  with  an  EINTHOVEN 
string  galvanometer,  in  his  transatlantic  stations. 


FIG.  340. 


The  incandescent  lamp  may  be  replaced  by  the  tube  devised  by  A. 
WEHNELT266  which  operates  in  the  same  manner.  The  incandescent 
cathode  of  this  tube  is  a  wire  coated  with  a  metallic  oxide,  and  the  anode 
is  a  hollow  aluminium  cylinder,  concentric  with  the  cathode. 

b.  H.  BRANDES267  has  found  that  it  is  very  advantageous  to  insert  an 
auxiliary  battery  or  cell,  E,  about  as  shown  in  Fig.  341,f  when  using 

*  TissoT265  describes  a  wave  indicator  using  rarified  air  (as  in  the  ZEHNDER  tube), 
which  he  found  to  be  less  sensitive  but  better  adapted  for  measuring  purposes, 
t  DI  and  Z>2  are  inductive  coils. 


DETECTORS 


285 


these  wave  indicators.  The  sliding  contact,  SC,  is  adjusted  until  the 
detector  is  operating  at  the  best  point  of  its  characteristic  [see  Art.  162a], 
thereby  greatly  increasing  the  sensitiveness  as  compared  to  operation 
without  the  auxiliary  cell.  This  method  has  lately  also  been  adopted  by 
FLEMING. 

c.  This  arrangement  had  in  fact  been  proposed  quite  some  time  ago 
by  DE  FOREST  in  his  so-called  "auction"  detector.  The  audion,  as  first 
constructed,  was  in  the  main  identical  with  FLEMING'S  construction,  ex- 
cepting that  DE  FOREST  made  use  of  an  auxiliary  cell  (E,  Fig.  341)  from 
the  very  first. 


Another  construction  of  DE  FOREST'S  " audion,"268  which  seems  to  be 
of  particular  excellence  is  that  shown  diagrammatically  in  Fig.  342. 
Here  F  is  the  metallic  filament  made  incandescent  by  the  current  from 
the  battery,  EI,  N  is  a  wire  grid  or  network  and  P  is  a  disc-shaped 
electrode.  All  three  electrodes  are  placed  in  an  exhausted  glass  bulb. 


5.  GENERAL  CONSIDERATION  OF  DETECTORS 

162.  The  Nature  of  the  Action  in  Various  Detectors. — a.  H.  BRANDES267 
has  shown  that  the  action  of  very  many  wave  indicators  may  be  gener- 
alized under  a  single,  common  point  of  view. 

All  these  wave  indicators  have  in  common  the  fact  that  they  do  not 
follow  OHM'S  law,  so  that  their  characteristic  [Art.  113]  instead  of  being  a 
straight  line,  is  an  irregular  curve. 

This  variation  includes  two  cases,  viz.: 

1.  The  curve  is  not  symmetrical  in  the  first  and  third  quadrants 
(Fig.  343),  i.e.,  the  current  is  not  the  same  for  any  two  potentials  of  equal 
amplitude  but  opposite  sign.  Hence,  if  the  potential  is  that  of  an  alternat- 
ing current  or  oscillation,  the  resulting  current  is  not  the  same  in  both 
directions.  Consequently  the  currents  in  two  directions  do  not  neu- 
tralize each  other  in  their  action  upon  a  galvanometer  which  shows  a 
deflection  without  the  insertion  of  an  auxiliary  battery;  likewise  a  tele- 


286 


WIRELESS  TELEGRAPHY 


phone  in  the  circuit  is  caused  to  produce  a  "click."*  The  detector  there- 
fore is  said  to  be  a  "rectifier."  f 

2.  The  characteristic  curve  is  symmetrical  in  the  first  and  third 
quadrants  (Fig.  344). 

In  this  case  the  oscillations  will  cause  equal  currents  to  flow  in  both 
directions,  so  that  the  detector,  per  se,  does  not  act  as  a  rectifier  and  a  gal- 
vanometer in  the  circuit  does  not  deflect. 

If  now,  however,  the  constant  potential  of  an  auxiliary  cell  is  impressed 
across  the  poles  of  the  detector,  an  increase  in  the  total  e.m.f.  due  to  the 
oscillations  causes  a  certain  increase  in  the  current  flowing  through  the 


FIG.  343. 


FIG.  344. 


detector;  an  equal  decrease  in  the  e.m.f.  due  to  the  oscillations,  however, 
does  not  produce  an  equal  decrease  in  the  current,  because  of  the  curva- 
ture of  the  characteristic.  Hence  the  effect  of  the  oscillations  is  to  change 
the  galvanometer  deflection  or  produce  a  click  in  the  telephone;  the  de- 
tector with  a  battery  in  series  acts  as  a  rectifier. 

The  rectifying  action  has  been  shown  by  BRANDES  to  be  greater  (1) 
the  steeper  the  characteristic  is  toward  the  axis  of  abscissae  at  the  point 
corresponding  to  the  e.m.f.  of  the  auxiliary  cell,  and  (2)  the  sharper  its 
curvature  is  at  this  point.  Hence,  in  using  this  class  of  detectors,  the 
auxiliary  e.m.f.  must  be  so  chosen  or  adjusted  as  to  permit  of  operation 
at  the  most  favorable  point  of  the  characteristic.^ 

b.  Many  investigations  of  the  characteristics  and  action  of  the  various 
detectors  have  been  made.269  It  has  been  shown  that  with  incandescent 
lamp,  electrolytic  and  the  various  crystal  and  thermal  detectors  (car- 
borundum, perikon,  graphite-galena,  copper-molybdenite,  anatase,  brook- 
ite)  the  characteristic  assumes  entirely  different  shapes  upon  reversal  of 
the  current.  Thus,  Fig.  345  shows  the  characteristic  of  the  highly  sen- 

*  This  explains  FERRIE'S  observation  of  the  fact  that  the  electrolytic  detector 
acts  as  a  wave  indicator  without  the  presence  of  a  battery  in  the  circuit. 

f  In  some  cases  current  passes  in  one  direction  only,  the  detector  acting  more  or 
less  as  a  valve. 

|  The  heating  devices  of  the  detectors  described  in  Art.  150c  have  a  similar  pur- 
pose; they  are  adjusted  to  give  the  temperature  at  which  the  characteristic  will  have 
its  most  favorable  curvature. 


DETECTORS 


287 


sitive  perikon  detector  [Art.  1606]  as  obtained  by  the  measurements  of 

W.    H.    ECCLES.269 

ECCLES  also  investigated  the  relation  between  the  sensitiveness  of 
various  detectors  and  the  value  of  the  impressed  auxiliary  e.m.f.  and  in 
almost  all  cases  found  that  maximum  sensitiveness  corresponded  to  a 
certain  value  of  the  auxiliary  e.m.f.  in  agreement  with  the  conclusions  of 
BRANDES. 

He  also  investigated  the  relation  between  the  D.C.  energy  delivered 
by  the  detector  to  the  telephone  and  the  energy  supplied  to  the  detector  by 
the  oscillations  and,  in  all  cases  coming  under  his  observation,*  he  found 

that  the  curve  representing  the  rela- 
tion between  D.C.  energy  delivered 
and  the  high  frequency  energy  sup- 


Red  Zinc  Oxide  -  Positive 


'-25 


0  ', 

0.2 

f 

*  — 

-~>K-^ 

, 

0          50          100         150      200 
0.2 

, 

0.4 

. 

0.6 

—^ 

0.8 
1.0 

Amp. 


Volt 


FIG.  345. 


High  Frequency  Energy 

FIG.  346. 


plied,  is  a  straight  line  which  does  not  quite  pass  through  the  common 
zero  point  (Fig.  346).  Hence  there  is  an  initial  value  above  which  the 
oscillating  energy  must  lie  to  produce  useful  D.C.  energy.  The  ratio  of 
the  D.C.  energy  to  the  high  frequency  energy  supplied,  i.e.,  the  efficiency  of 
the  detector,  was  found,  under  the  conditions  of  the  tests  made  by  ECCLES, 
to  be  13  per  cent,  for  the  electrolytic  detector  (sensitive  electrode  0.006 
mm.  thick,  sulphuric  acid  electrolyte),  9.3  per  cent,  for  the  carborundum 
detector,  13  per  cent,  for  the  perikon  detector  and  about  3  per  cent,  for 
graphite-galena,  the  figures  being  the  maximum  obtained  in  each  case. 

These  tests  are  of  particular  value,  because  the  conditions  (frequency, 
energy)  encountered  in  the  actual  practice  of  radio-telegraphy  were  re- 
tained as  closely  as  possible,  which  can  by  no  means  be  stated  of  all  the 
investigations  which  have  been  made  in  this  field  of  work. 

163.  What  do  the  Different  Types  of  Detectors  React  Upon?270— a. 
Assume  that  only  a  single  oscillation  (say  a  single  discharge  from  a  con- 
denser circuit)  acts  upon  a  wave  indicator.  Then: 

1.  The  reaction  of  the  thermal  detectors,  and  to  some  extent  also  of 
mercury  coherers,  depends  upon  the  heat  developed  within  them,  i.e., 

upon  the  current  effect  -T^TJ  '  ^o2. 

4  A' a 


*  Iron-mercury,  electrolytic  detector,   carborundum,  perikon  detector,  graphite- 
galena. 


288  WIRELESS  TELEGRAPHY 

2.  For  magnetic  detectors,  the  amplitude  (or  the  maximum  amplitude 
[Arts.  56c  and  61c])  of  the  current,  /0  (or  Imax)  is  probably  the  determining 
factor. 

3.  For  rectifying  detectors,  the  quantity  of  electricity  passing  in  one 
direction  in  excess  over  that  quantity  passing  through  the  detector  in  the 
other  should  be  the  determining  factor.     This  excess  quantity  depends 
not  only  upon  the  amplitude  of  the  potential  occurring  between  the  poles 
of  the  detector,  but  also  upon  the  damping.     Where  the  rectifying  action 
is  complete  so  that  the  resultant  flow  of  current  is  unidirectional,  this 

quantity  is  approximately*    =  —TTJ  •  I0)  hence  like  the  current  effect,  it 

varies  as  v^?  but  it  varies  as  IQ,  not  as  /o2.f 

With  the  metallic  coherers,  a  certain  minimum  potential  difference  be- 
tween the  electrodes  must  exist  to  produce  a  reaction.  However,  in  order 
to  cause  a  large  change  in  the  resistance,  as  is  required  in  practice,  a  certain 
current  effect  must  be  reached.  In  this  respect,  therefore,  the  coherer 
is  not  unlike  the  thermal  detectors,  for  its  action  also  depends  upon  the 
decrement  of  the  oscillations  as  well  as  upon  the  amplitude. 

b.  Assume  that  a  very  rapid  sequence  of  oscillations  (e.g.,  undamped 
oscillations  or  damped  oscillations  of  very  high  discharge  frequency  acts 
upon  the  detector.  Then  there  are  two  possible  cases,  viz., 

1.  The  effect  upon  the  wave  indicator  is  determined  entirely  or  almost 
entirely  by  the  first  oscillation.     The  oscillations  which  follow  do  not 
materially  aid  the  action.     This  is  the  case,  e.g.,  with  the  coherer  and 
with  MARCONI'S  magnetic  detector. 

2.  The  effect  upon  the  wave  indicator  is  the  sum  of  the  effects  of  the 
successive  oscillations  in  the  series.     This  undoubtedly  is  the  case  with 
the  thermal  detectors,  the  magnetic  detectors  of  the  WALTER  type  [Art. 
154],   to  a    certain  extent  also  with  the  electrolytic    detectors  of  the 
SCHLOMILCH  type  and  in  general,  with  all  those  to  which  Art.  162  applies. 

In  considering  this  question,  however,  it  is  important  to  distinguish 
sharply  between  the  effect  upon  the  detector  and  that  upon  the  receiving 
apparatus.  If,  e.g.,  the  discharge  frequency  is  increased,  while  the 
amplitude  and  damping  remain  constant,  there  is  no  doubt  that  the 
effect  upon  a  thermal  detector,  in  other  words,  that  the  direct  current 
delivered  by  it  will  also  increase,  other  things  being  equal.  Nevertheless 
the  intensity  in  the  receiving  telephone  [see  Art.  165]  may  decrease  with 
the  increased  discharge  frequency.  The  amplitude  of  the  oscillations  of 

_d 

*  The  exact  value  is  —£~T  •  -; •=•, 

irN        1  —  e  d 

t  It  seems  that  the  action  of  certain  detectors,  which  are  generally  considered 
as  perfect  rectifiers,  depends  upon  the  current  effect.  If  that  is  the  case,  then  these 
detectors  can  not  be  pure  rectifiers. 


DETECTORS  289 

the  telephone  diaphragm,  depends  not  only  upon  the  amplitude  of  the 
D.C.  impulses  but  also  upon  their  variation  with  time  and  upon  the 
length  of  the  intervals  between  them;  if  these  intervals  become  too  short 
the  amplitude  of  the  telephone  diaphragm's  motion  may  decrease. 

c.  If  the  individual  oscillations  follow  one  after  the  other  with  rela- 
tive slowness  (e.g.,  damped  oscillations  produced  by  means  of  a  resonance 
transformer)  then  not  only  the  wave  indicator,  but  also  the  method  of 
reception  will  determine  whether  or  not  the  effects  of  the  individual 
oscillations  are  summed  up.  Thus  when  receiving  with  a  telephone  only 
the  effect  of  a  single  oscillation  comes  into  question,  whereas  with  a 
siphon  recorder  [Art.  167a]  or  similar  devices  the  result  is  a  summation  of 
the  individual  effects. 

164.  Testing  the  Sensitiveness  of  Detectors.271 — A  general  statement 
as  to  the  relative  sensitiveness  of  two  detectors  is  often  impossible  when  the 
detectors  are  of  a  different  type. 

a.  The  ratio  moreover  may  vary  as  the  character  of  the  oscillations 
used  for  the  test  varies;  thus  it  may  be  different  for  undamped  than  for 
damped  oscillations,  and,  again,  with  damped  oscillations  it  will  depend 
upon  the  amplitude,  the  decrement  and  the  discharge  frequency.  At 
twenty  discharges  per  second,  a  good  coherer  will  receive  at  practically 
the  same  range  as  a  thermal  detector,  but  at  1000  discharges  per  second, 
with  the  same  transmitted  energy  and  a  corresponding  decrease  in  ampli- 
tude, the  range  of  the  thermal  detector  will  be  over  five  times  that  of 
the  coherer  (COUNT  Anco160). 

Hence  where  it  is  desired  to  determine  which  of  two  detectors  is  the 
most  sensitive  for  service  from  a  given  station,  it  is  advisable  to  let  a 
closed  oscillating  circuit  whose  oscillations  have  just  about  the  same 
time  variation  and  discharge  frequency  as  the  waves  of  the  station  in 
question,  act  upon  the  detectors.  The  alternative  method  of  using  any 
of  the  so-called  station  testers  or,  perhaps,  as  is  frequently  done,  of  using 
an  interrupted  direct  current  to  act  upon  the  detectors,  can  only  give 
very  questionable  results. 

6.  Different  arrangement  of  the  receiving  circuits  may  also  greatly 
affect  the  relative  sensitiveness  of  two  detectors.  Thus,  the  results  may 
differ  if  the  detectors  are  connected  to  a  weakly  damped  receiving  con- 
denser circuit  as  compared  to  inserting  them  in  a  closed  (aperiodic)  cir- 
cuit [see  Art.  175  et  seq.]. 

c.  Finally  the  receiving  apparatus  itself  may  greatly  influence  the 
relative  sensitiveness  and  hence  the  attainable  range.  Thus  telephone 
reception  may  give  quite  different  results  than  a  recording  receiver  involv- 
ing the  use  of  a  relay. 

All  these  factors  must  be  carefully  considered  in  comparing  detectors 
as  to  their  sensitiveness. 
10 


290 


WIRELESS  TELEGRAPHY 


6.  RECEIVING  APPARATUS 

165.  Telephone  Reception. — The  receiving  apparatus  assumes  its 
simplest  forms  with  those  wave  indicators  which  are  self -restoring  upon 
cessation  of  the  oscillations  or  which  at  least  are  able  to  immediately 
indicate  a  new  oscillation  (including  all  wave  indicators  with  the  excep- 
tion of  the  metallic  coherer).  With  these  a  telephone  can  be  used  as  the 
receiver. 

a.  The  simplest  method  of  connection  for  wave  indicators  without  an 
auxiliary  cell,  is  shown  diagrammatically  in  Fig.  347*  and  for  wave  indi- 
cators with  an  auxiliary  cell,  in  Fig.  348.  f  In  these  J 
is  the  wave  indicator,  T  the  telephone,  E  the  auxiliary 
cell  and  L  the  receiving  circuit  containing  /. 

A  telephone  thus  connected  when  held  to  the  ear 
produces  a  clicking  sound  at  each  discharge  of  the  trans- 
mitter, if  the  discharge  frequency  is  low.  If  this  fre- 
quency is  high,  either  a  pure  tone  is  heard  in  the  tele- 
phone in  which  case  the  discharge  frequency  is  regular 
and  within  the  range  of  audibility,  or  otherwise  a 
buzzing  discordant  sound  is  heard. 

The  letter  "a"  ( in  the  MORSE  code)  is  heard  in 

the  telephone  as  a  short  (dot)  click,  buzz  or  tone  followed 
by  a  longer  sound  (dash)  of  the  same  character.  Tele- 
grams can  therefore  be  received  by  means  of 
the  ear,  just  as  with  the  sounders  or  buzzers 
used  in  wire  telegraphy. 

&.  For  wave  indicators  with  an  auxiliary  cell 
the  arrangement  requires  a  slight  modification. 
Firstly,  it  is  advantageous  to  impress  the 
particular  e.m.f.  at  which  the  indicator  is 
most  sensitive  [Art.  162a].  To  adjust  for 
this,  a  high  resistance,  AB  (Fig.  349),  is  con- 
nected across  the  terminals  of  the  cell  E,  which 
should  have  a  relatively  high  e.m-.f.,  and  is 
provided  with  a  sliding  contact,  K.%  Then  any  desired  voltage,  up  to 
that  of  the  cell,  E,  can  be  obtained  between  K  and  B  and  hence  across 
the  terminals  of  the  wave  indicator,  J. 

Furthermore,  the  connections  of  Fig.  348  would  have  the  disadvantage 
of  causing  the  oscillation  currents  in  the  circuit  L  to  partly  branch  off 

*  The  receiving  circuit,  L,  must  of  course  form  a  complete  closed  circuit.  If 
the  telephone  is  connected  in  parallel  to  the  wave  indicator,  then  the  circuit  L  must 
have  a  condenser  (block  condenser  [Art.  41d])  in  it,  in  order  to  prevent  the  direct 
current  of  the  wave  indicator  from  flowing  into  it. 

t  But  see  6. 

J  This  is  simply  a  "potentiometer"  connection. 


\\£ 


FIG.  347. 


FIG.  348. 


DETECTORS 


291 


into  the  telephone  circuit  TE  (Fig.  348)  so  that  only  a  part  would  pass 
through  the  wave  indicator.  To  prevent  this  two  choke  coils,  DI  and  D2 
in  Fig.  349,  are  inserted  at  the  junction  points  to  block  the  path  of  the 
oscillations  through  the  telephone  circuit  [Art.  416]. 


FIG.  349. 

166.  Amplification   of   the    Sound   in   Telephone    Reception. — Two 

devices  which  have  been  successfully  used  for  intensifying  the  sound 
produced  in  the  receiving  telephone,  are  the  telephone  relay  of  S.  G. 
BROWN  and  the  so-called  "  sound  intensifier"  of  the  TELEFUNKEN  Co. 


FIG.  350. 


FIG.  351. 


In  both  apparatus,  the  detector  current  first  acts  upon  a  kind  of  micro- 
phone and  the  microphone  current  then  flows  through  the  telephone. 

a.  The   Brown   telephone   relay272   is    illustrated   in   Figs.    350   and 
351,  the  latter  showing  the  connections.     N  and  S  are  the  poles  of  a 


292 


WIRELESS  TELEGRAPHY 


horseshoe  magnet,  on  which  two  soft  iron  cores  whose  windings  are  marked 
K  and  H  rest.  P  is  a  steel  tongue  carrying  a  small  osmium-iridium 
plate  0,  which  lightly  touches  a  contact  point  M  also  consisting  of  an 
osmium-iridium  alloy.  C  is  a  dry  cell  whose  circuit  contains  the  contact 
OMj  the  winding  K  and  the  telephone  T.  The  current,  whose  effect 
upon  the  telephone  is  to  be  amplified,  is  sent  through  the  winding  H. 
This  causes  the  steel  tongue,  P,  which  takes  the  place  of  the  telephone 
diaphragm  to  vibrate,  thereby  alternately  strengthening  and  weakening 
the  current  in  the  circuit  COMKT  in  unison  with  the  oscillations,  with 
the  result  that  a  materially  stronger  effect  is  produced  upon  the  telephone, 
Tj  than  if  the  current  in  H  were  sent  direct  through  T. 

Tests  made  by  the  British  Admiralty  and  Post  Office  Departments 
indicated  that  this  telephone  relay  doubled  the  range.  Messages  whose 
existence  could  not  be  discovered  with  the  ordinary  telephone  apparatus 


Detector  Current 


FIG.  352. 

were  easily  received  with  the  BROWN  relay.  During  tests  made  between 
the  Clifden  and  Poole  stations  in  Ireland,  by  using  two  relays  connected 
in  series  it  was  possible  to  clearly  hear  messages  2  m.  away  from  the 
receiver,  while  in  the  ordinary  receiver  without  relay  the  same  message 
could  just  be  discerned  as  a  slight  noise. 

b.  In  the  Telefunken  Tone  Intensified™  which  is  adapted  only  for  use 
with  a  tone  transmitter,  the  detector  current  is  conducted  to  a  small 
electromagnet  (Ti,  Fig.  352)  having  a  large  number  of  turns.  In  the 
field  of  the  magnet  there  is  a  small  armature  A  i,  whose  natural  frequency 
of  vibration  corresponds  to  the  frequency  of  the  detector  current  and 
hence  to  the  tone  of  the  transmitter.  This  resonant  armature  presses 
against  a  microphone  contact,  MI,  which  is  in  the  circuit  of  a  local 
battery,  EI.  This  circuit  also  contains  an  electromagnet,  Tz,  constructed 
identically  as  TI.  The  current  flowing  through  T%  pulsates  at  the  same 
frequency  as  the  detector  current  flowing  through  TI,  but  has  a  much 
greater  amplitude.  Hence  the  armature,  At,  which  is  identical  with  Ai, 
vibrates  more  violently  than  A  i,  so  that  the  pulsations  in  circuit  II,  which 
contains  the  microphone  contact,  Mz,  local  battery,  Ez,  and  electromagnet, 
Ta,  become  still  greater  than  in  circuit  /.  Armature  As  and  microphone 


DETECTORS  293 

contact  M3  then  produce  another  increase  in  the  pulsations.  This  three- 
fold amplification  is  sufficient  to  produce  a  current  of  about  10~2  amp.  in 
circuit  777,  which  contains  the  receiving  telephone,  when  the  detector 
current  is  only  from  10~7  to  10~8  amp. 


FIG.  353. 


In  conjunction  with  the  intensifier  it  is  customary  to  use  a  special 
loud-speaking  telephone  (LT,  Fig.  352),  having  an  acoustic  resonator  at 
the  opening  of  its  mouthpiece,  the  resonator  being  tuned  to  the  tone  of  the 
transmitter,  thus  causing  a  further  amplification. 


294 


WIRELESS  TELEGRAPHY 


This  extensive  application  of  mechanical 
and  acoustic  resonance  together  with  the 
microphone  amplification  results  in  a  very 
marked  increase  in  the  sound  intensity.  Fig. 
353  shows  the  construction  of  this  sound  in- 
tensifier,  wnich  has  found  a  place  in  many 
stations. 

167.  Automatic  Recording  of  Messages. — 
With  certain  detectors  (e.g.,  thermal  detec- 
tors, LODGE  and  MUIRHEAD'S  mercury 
coherer)  the  receiving  telephone  can  be  re- 
placed by  a  well  damped  galvanometer.  If 
connected  in  series  with  the  wave  indicator 
and  a  battery,  the  galvanometer  deflects  and, 
as  soon  as  the  oscillations  cease,  returns  to 
its  zero  position.  This  makes  a  direct  record- 
FIG.  354.  ing  of  telegrams  possible  in  various  ways. 

LODGE  and  MUIRHEAD'S  method*  as  applied  to  their  mercury 


L_J~l 


a 


coherers  is  as  follows  (Fig.  354). f  A  pen  or  pencil  is  attached  to  the 
movable  coil,  $,  of  a  galvanometer  and 
touches  a  paper  strip  or  tape  which  is 
moved  by  clockwork,  as  in  the  ordinary 
MORSE  recorder.  As  the  galvanometer  coil 
rotates  the  pen  or  pencil  is  moved  perpen- 
dicularly to  the  direction  of  motion  of  the 
paper. 

As  long  as  the  wave  indicator  is  not 
subjected  to  oscillations,  the  galvanometer 
coil  remains  stationary  and  the  record  is 
simply  a  continuous  straight  line  (a  to  b  in 
Fig.  355).  A  brief  excitation  of  the  wave 
indicator — i.e.,  a  MORSE  dot — produces  the 
effect  shown  at  b  in  Fig.  355,  while  a  dash 
appears  as  shown  at  c-d. 

b.  Later  the  movable  coil  galvanometer 
used  by  LODGE  and  MUIRHEAD  was  re- 
placed by  the  much  more  sensitive  and 

*  The  complete  outfit  is  frequently  called  "Siphon  recorder." 
f  M  is  the  horseshoe  magnet  of  the  movable  coil  galvanometer. 


DETECTORS 


295 


less  sluggish  EINTHOVEN  string  galvanometer  and  a  photographic  record 
of  the  message  made. 

The  EINTHOVEN  string  galvanometer  (FiG.  356)*  as  is  well  known, 
consists  of  a  fine  wire  (Wollaston  wire,  fine  metal  strip  or  conductive 
quartz  fiber),  which  is  stretched  in  the  gap  between  the  poles  of  a  magnet 
perpendicularly  to  the  magnetic  flux  lines  (between  F  and  M  in  Fig.  356). 
If  current  is  passed  through  this  wire,  the  latter  will  be  displaced  from  its 
normal  position  in  a  direction  perpendicular  to  its  axis  and  to  the  mag- 
netic flux  lines. 

The   wire   moves  in  front  of  a  narrow  illuminated  slit 
(Fig.  357).     A  photographic  reproduction  of  the  slit  and  wire 
on  a  sensitive  film  passing  perpendicularly  across  the  slit, 
appears,  on  the  negative,  as  a  broad  dark   band,   with  a 
fine  light  line  (the  wire)  through  its  center.     If,  however,  the 
wire  is  displaced  from  its  normal  position,  first  for  a  brief 
instant,  and  then  for  a  somewhat  longer  duration,  the  photographic 
record  will  appear  as  a  light  line  similar  to  the  line  of  Fig.  355,  i.e.,  the 
characteristic  dot  and  dash. 

A  complete  photographic  recorder275  is  illustrated  in  Fig.  358. f  At 
the  left  is  the  galvanometer,  whose  wire  and  slit  are  illuminated  by  a 
small  incandescent  lamp  (of  which  the  plug  and  flexible  lead  are  visible). 


FIG.  357. 


FIG.  358. 

The  micro-photographic  lens  is  placed  in  the  metal  tube,  at  the  right  is 
the  camera  and  in  back  of  this  is  the  case  in  which  the  strip  of  sensitive 

*  The  cut  is  taken  from  a  catalogue  of  PROF.  EDELMANN  &  SON  (Munich)  who  make 
this  and  also  more  modern  types  of  galvanometer.  The  firm  of  E.  HuTH274  makes 
still  another  construction  of  the  instrument. 

f  Construction  of  the  C.  LORENZ  Co.  Other  receiving  apparatus  of  the  same  kind 
are  constructed  along  very  similar  lines. 


296 


WIRELESS  TELEGRAPHY 


film  which  is  moved  by  clockwork,  is  developed  and  fixed.  It  has  already 
been  mentioned  that  MARCONI  also  uses  the  EINTHOVEN  string  galvan- 
ometer in  his  transatlantic  stations  [Art.  16 la]. 


FIG.  359. 

c.  In  place  of  a  galvanometer,  a  relay  (RiRi,  Fig.  359)  which  opens 
and  closes  the  circuit  of  a  MORSE  recorder,  M,  and  local  battery,  Ez 
(Fig.  359),*  can  be  used. 


FIG.  360. 

The  construction  of  a  polarized  relay  which  is  customarily  used  for 
this  purpose,  is  no  doubt  evident  from  the  diagram  of  Fig.  360  (a,  view 
from  above;  6,  view  from  side).  M  is  a  permanent  steel  magnet,  with  one 

*  In  regard  to  the  resistance,  w,  in  Fig.  359,  see  Art.  1686.  The  choke  coils,  which 
here  also  are  inserted  to  protect  the  relay  from  the  oscillations  in  the  main  circuit, 
L,  have  been  omitted  in  the  diagram. 


DETECTORS  297 

pole  at  A,  the  other  at  B.  On  the  latter  are  placed  the  iron  cores,  BiB2, 
of  the  coils,  Si  and  S2,  which  are  in  circuit  with  the  wave  indicator  and  a 
battery  through  the  leads  i\.  U  is  a  movable  armature  which  makes 
contact  with  C/i  closing  and  opening  the  circuit  i  which,  in  addition  to  the 
MORSE  recorder  (M}  Fig.  359)  contains  a  battery  of  one  or  more  cells. 

A  relay  of  this  kind  is  quite  sensitive.  Thus  the  TELEFUNKEN276 
relays  of  this  type  were  stated  to  respond  positively  when  operated  with 
1.4  volts  and  a  series  resistance  of  100,000  ohms.  So  high  a  degree  of 
sensitiveness  is  attainable  only  if  the  adjustments  for  the  distance  BiB-2 
and  the  contacts  C/iC/2  are  particularly  fine.  Furthermore,  the  armature 
U  must  be  balanced  with  excep- 
tional care  to  prevent  interference 
from  outside  disturbances  or  from 
the  rolling  of  the  ship  when  used  at 
sea. 

The  TELEFUNKEN  Co.  formerly 
used  a  magnetic  adjustment276  on  its 
relays.  By  turning  a  piece  of  soft 
iron  mounted  on  the  casing  of  the 
relay,  the  magnetic  field  within  was 
varied,  thus  providing  the  desired 
regulation.  This,  moreover,  has  the 
advantage  of  entirely  enclosing  the 

relay  in  its  casing,  so  that  its  other  -pio.  361. 

adjustments  remain  fixed  once  and 
for  all.     The  external  appearance  of  the  relay  is  shown  in  Fig.  36 1.276 

The  reason  for  not  simply  inserting  the  MORSE  apparatus  directly 
in  the  same  circuit  as  the  relay  is  as  follows :  On  the  one  hand,  the  poten- 
tial existing  across  the  terminals  of  any  of  the  usual  wave  indicators  in 
their  unexcited  condition  is  limited  to  a  certain  maximum  value,  above 
which  (at  most  2  volts,  usually  much  less)  it  must  not  be  permitted  to 
rise.  On  the  other  hand,  only  very  small  currents  (usually  considerably 
below  Jfooo  amp.)  can  be  allowed  to  flow  through  the  majority  of  detec- 
tors during  excitation  without  harming  them.  This  combination  of  very 
low  voltage  with  very  small  current  is  generally  sufficient  to  operate  a 
sensitive  relay  but  not  a  MORSE  recorder. 

d.  Some  detectors  in  fact  can  not  stand  a  current  sufficient  to  operate 
a  sensitive  polarized  relay.  Hence,  when  it  was  desired  to  automatically 
record  telegrams  with  such  a  detector,  it  was  formerly  necessary  to 
employ  a  photographic  method  with  the  aid  of  a  galvanometer.  With  the 
sound  intensifier  of  the  TELEFUNKEN  Co.,  however,  as  long  as  the  essen- 
tial requirements  of  constant  and  sufficiently  high  discharge  frequency  in 
the  transmitter  ("tone  transmitter")  are  filled,  it  is  possible  to  use  the 
more  convenient  MORSE  recorder. 


298 


WIRELESS  TELEGRAPHY 


The  connections273  for  this  purpose  are  sketched  in  Fig.  362.  The 
microphone  current  of  the  third  amplifier  (///  in  Fig.  352)  consisting  of 
D.C.  with  superimposed  A.C.,  instead  of  being  led  directly  to  the  loud- 
speaking  telephone  (LT,  Fig.  352),  is  sent  through  a  small  transformer, 
TF  (Fig.  362),  by  way  of  the  throw-over  switch,  U.  A  pure  alternating 
e.m.f.  is  induced  in  the  transformer  secondary.  In  the  secondary  cir- 
cuit, however,  is  a  rectifier,  V,  so  that  current  flows  through  it  and 


To  Loud-Si 


FIG.  362. 

through  the  relay,  R,  in  one  direction  only.     This  unidirectional  current, 
however,  is  strong  enough  to  actuate  the  polarized  relay. 

168.  Recording  Apparatus  for  the  Metallic  Granular  Coherer. — The 
recording  devices  described  in  what  has  preceded,  suffice  for  wave  indi- 
cators which  are  self-restoring,  but  not  for  the  metallic  granular  coherer. 
The  latter,  if  connected  with  one  of  these  devices,  would  become  conduc- 
tive at  the  first  oscillation  and  remain  so  indefinitely;  the  relay  in  circuit 
with  the  coherer  would  then  remain  closed  and  the  record  would  be  a 
continuous  straight  line. 


FIG.  363. 

a.  Hence,  it  is  absolutely  necessary  to  have  a  so-called  "tapper"  to 
restore  the  coherer  to  its  normal  condition  after  each  oscillation  or  wave 
train.  As  is  evident  from  the  diagram  of  Fig.  363,  the  construction  of  the 
tapper  is  simply  that  of  the  ordinary  electric  bell  or  buzzer. 

In  the  method  of  connection  shown  in  Fig.  364,*  which  represents  a 
standard  coherer  receiving  outfit,  current  flows  through  the  coherer 
immediately  before  it  is  tapped.  As  soon  as  the  tapper  strikes  the 

*  EiE2  are  galvanic  cells,  K  is  the  tapper,  R  the  relay,  UUi  the  "make  and  break" 
contact  of  the  relay,  M  the  MORSE  recorder,  W  a  bell  or  sounder.  P  is  a  throw  over 
switch  for  cutting  in  either  the  MORSE  recorder,  M,  or  the  sounder,  W, 


DETECTORS 


299 


coherer,  this  current  is  interrupted  within  the  coherer.  In  spite  of  all 
precautions  [see  6],  this  will  be  accompanied  by  minute  sparking  which 
causes  deterioration  of  the  granules;  this  tends  to  prevent  easy  restora- 
tion of  the  coherer  and  to  reduce  its  life  or  duration  of  usefulness.  To 
meet  this  difficulty,  the  TELEFUNKEN  Co.  and  others  arranged  the 
tapper  so  as  to  open  the  coherer  circuit  just  before  striking  the  coherer, 
so  that  the  tapping  always  occurs  at  zero  current. 

6.  In  the  method  of  connection  shown  in  Fig.  364  there  are  three 
places  where  circuits  containing  coils  wound  on  iron  cores,  i.e.,  having 
high  self-induction,  are  opened.  Hence,  quite  high  potentials  arise  and 


FIG.  364. 


sparks  occur  at  the  points  of  interruption.  This  may  result  in  the  forma- 
tion of  electromagnetic  waves  which  act  upon  the  wave  indicator.  But 
even  if  this  does  not  occur,  the  interruption  of  the  relatively  large  cur- 
rents may  induce  an  e.m.f.  in  the  circuit  of  the  wave  indicator,  sufficient  to 
cause  the  latter  to  respond  to  it. 

This  difficulty  is  usually  avoided  or  minimized  by  placing  in  parallel 
with  the  break  in  the  circuit  and  with  the  iron-core  windings,  non- 
inductive  resistances  [as,  e.g.,  w  in  Fig.  359]  of  suitable  ohmic  value  or 
polarized  cells  (e.g.,  two  platinum  wires  as  electrodes  in  diluted  sulphuric 
acid),  or  also  condensers  of  proper  size,  sometimes  in  conjunction  with 
non-inductive  resistances. 

169.  Call  Signals.  —  When  it  is  desired  to  transmit  a  message  instantly 
and  perhaps  to  obtain  an  immediate  reply  (as  in  military  work),  it  is 
essential  to  have  some  method  of  calling  the  receiving  station.  This  is 
also  of  great  importance  when  ships  at  sea  are  in  danger.  Otherwise,  for 


300  WIRELESS  TELEGRAPHY 

ordinary  radio-traffic,  a  call  signal  is  not  absolutely  essential.  More- 
over there  are  recording  receivers  so  arranged  that  their  clockwork  is 
automatically  started  when  a  telegram  arrives  and  stops  as  soon  as  the 
telegram  is  completed.* 

a.  Where  a  relay  is  provided  to  operate  the  MORSE  recorder,  it  is  com- 
paratively a  simple  matter  to  connect  an  electric  bell  (W  in  Fig.  364)  as 
a  call  signal. 

b.  However,  when  the  use  of  a  relay  is  objectionable  or  undesirable 
in  view  of  its  added  complication  to  the  equipment,  so  that  a  simple 
telephone  receiver  is  used,   the  problem  is  somewhat  different.     The 
TELEFUNKEN  Co.  has  found  a  simple  solution  for  it277  as  follows:    A 
moving  coil  galvanometer  of  high  sensitiveness,!  whose  coil  and  the 
pointer  connected  thereto  are  very  sluggish,  is  placed  in  the  detector  cir- 
cuit.    When  the  pointer  deflects  up  to  a  certain  angle,  it  runs  into  a 
contact  wheel  which  is  turned  by  a  small  clockwork  and  which  holds  the 
pointer  fixed.     This  closes  a  circuit  containing  the  call  bell  and  a  battery, 
so  that  the  bell  rings  until  the  operator  at  the  receiving  station  breaks 
the  contact.     The  sluggish  motion  of  the  movable  coil  and  pointer  makes 
it  necessary  for  the  transmitting  station  to  send  out  a  long  dash  lasting 
say  10-12  seconds,  during  which  time  the  transmitter  continues  to  send 
out  waves  having  a  cumulative  action  upon  the  galvanometer.     This 
prevents  atmospheric  disturbances  of  short  duration  from  actuating  the 
call  signal  and  unnecessarily  calling  the  station  operators  to  the  receiver. 

170.  Comparison  of  the  Different  Kinds  of  Detectors. — a.  The  main 
points  to  be  considered  in  determining  the  practical  usefulness  of  various 
detectors  are  as  follows: 

1.  Sensitiveness. 

2.  Reliability  in  operation. 

3.  Simplicity  in  operation. 

4.  Simplicity  of  the  necessary  auxiliary  apparatus. 

5.  Possibility  of  using  a  call  signal. 

6.  Possibility  of  using  a  recording  receiver. 

7.  Rapidity  of  telegraphing  attainable. 

b.  As  to  the  sensitiveness,  a  practical  consideration  of  particular 
importance  is  whether  the  action  of  a  series  or  sequence  of  successive 
waves  (wave  trains)  is  cumulative  or  not  [Art.  163]. 

This  is  not  the  case  with  the  metallic  granular  coherer.  As  it  is  cus- 
tomary in  modern  practice  to  work  with  a  relatively  high  discharge  fre- 
quency and  relatively  low  energy  per  discharge,  this  alone  has  been 
sufficient  to  displace  the  coherer  from  practical  use.f 

*  The  use  of  such  automatic  recorders  is  greatly  limited  in  wireless  telegraphy,  as 
atmospheric  disturbances  constantly  actuate  the  clockwork. 
t  1  scale  division  =  10~7  amp. 
t  Except  in  certain  special  cases  [e]. 


DETECTORS  301 

c.  To  this,  however,  is  added  another  undesirable  property  of  the 
coherer.     It  seems  that  with  the  carbon  and  graphite  coherers,  as  well  as 
with  the  metallic  granular  coherers,  the  reliability  or  certainty  of  operation 
becomes  greatly  reduced  as  the  sensitiveness  is  increased,  a  change  which 
is  not  nearly  so  marked  in  other  wave    indicators.     Operators    have 
always   suffered  from   the   capriciousness,    one  might  say,  of  any  very 
sensitive  coherers. 

High  sensitiveness  is  of  practical  value  only  when  combined  with  suffi- 
cient reliability  in  operation.  Little  can  be  stated  on  this  subject  as  to 
the  various  wave  indicators,  as  this  depends  not  merely  upon  the  par- 
ticular type  of  indicator,  but  to  a  great  extent  upon  the  care  taken  in 
the  construction  of  the  individual  indicator. 

Non-sensitiveness  to  mechanical  jarring  and  above  all  to  momentary 
overloading  caused  by  atmospheric  disturbances  or  the  proximity  of  a 
powerful  transmitter  is  essential  to  reliability.  Accordingly,  wave  in- 
dicators having  a  point  contact,  as,  e.g.,  certain  of  the  thermal  detect- 
ors, are  dangerous  in  both  respects,  while  electrolytic  detectors  like 
that  of  SCHLOMILCH  are  non-sensitive  to  jarring,  but  very  sensitive  to 
overloading. 

d.  Operation  is  simplest  with  those  detectors  which,  when  once  adj  usted, 
require  no  further  regulation  (some  of  the  crystal  detectors,  magnetic 
detectors,  incandescent  lamp  detectors).     Wave  indicators,  whose  sen- 
sitiveness depends  largely  upon  the  pressure  at  the  point  of  contact,  are 
apt  to  require  frequent  readjustment.*     For  this  skilled  operators  are 
needed  and  it  is  often  the  cause  of  poor  service. 

As  to  the  handling  of  the  receiving  apparatus,  the  use  of  a  polarized 
relay  involves  considerable  skill  and  care  in  making  the  adjustment  and 
readjustments.  In  this  respect  the  photographic  recording  receivers 
have  the  advantage;  but  with  these,  the  string  of  the  EINTHOVEN  galvan- 
ometers requires  equally  careful  adjustments. 

e.  As  to  simplicity  of  the  receiving  apparatus,  it  is  evident  that 
receivers  involving  any  moving  parts  operated  by  clockwork  are  at  an 
inherent  disadvantage.     MARCONI'S  magnetic  detector  has  the  additional 
disadvantage  of  occupying  a  large  amount  of  space,  which  however  is  not 
so  important  in  large  land  stations. 

The  number  of  necessary  apparatus,  however,  aside  from  the  case  of 
the  coherer,  which  is  disadvantageous  from  this  viewpoint  also,  depends 
not  so  much  upon  the  type  of  wave  indicator  as  upon  the  object  in  view. 
If  only  telephonic  reception  is  desired,  the  apparatus  becomes  as  simple 
as  possible,  but  recording  the  messages  and  using  a  call  signal  always 

*  The  fact  that  readjustment  for  maximum  sensitiveness  is  possible  with  these 
wave  indicators  comprises  an  advantage  from  another  point  of  view.  For  those 
indicators  in  which  such  readjustment  is  impossible  may  become  worthless  after  a 
sufficiently  severe  atmospheric  disturbance. 


302  WIRELESS  TELEGRAPHY 

complicates  the  receiving  apparatus,  no  matter  what  kind  of  a  wave 
indicator  is  used. 

The  great  simplicity  and  sensitiveness  of  the  telephone  receiver  explains 
why  this  has  become  the  rule,  the  recording  receiver  the  exception,  even 
though  the  latter  has  certain  decided  advantages.  The  sensitiveness 
and  reliability  of  telephonic  reception  is  largely  dependent  upon  psycho- 
logical factors  in  the  operator  and  is  easily  interfered  with  by  external 
noises;*'278  the  reliability  of  a  recording  receiver  depends  only  upon  the 
excellence  of  the  apparatus  and  it  always  furnishes  a  positive  document  of 
the  received  message. 

/.  Formerly  the  possibility  of  applying  a  call  signal  and  a  recorder  drew 
sharp  lines  between  the  various  wave  indicators.  This  distinction,  how- 
ever, has  gradually  disappeared.  The  method  of  calling  [Art.  169]  intro- 
duced by  the  TELEFTJNKEN  Co.  seems  to  be  adaptable  to  nearly  all  wave 
indicators  of  practical  value.  And  as  to  recording  received  messages, 
there  appear  to  be  two  methods  applicable  to  all  wave  indicators,  either 
by  means  of  an  EINTHOVEN  galvanometer  (photographic  recording)  or 
by  means  of  the  TELEFUNKEN  sound  intensifier,  which  latter,  however, 
presupposes  tone  transmission. 

g.  All  the  various  wave  indicators  and  recording  devices  are  capable 
of  responding  to  the  speed  of  telegraphing  obtainable  by  manual  operation 
of  the  transmitting  key  or  relay  key.  With  the  high  speeds  attained  by 
means  of  automatic  keys  and  rapid  telegraph  devices  [Art.  117 c],  the  use 
of  the  metallic  granular  coherer,  which  involves  the  setting  into  operation 
of  a  series  of  mechanical  apparatus  is  of  course  out  of  the  question.  So 
far  as  the  author  knows,  the  limit  of  permissible  speed  in  transmission  has 
not  been  reached  with  any  of  the  other  wave  indicators  used  in  practice. 

However,  the  limitation  in  the  permissible  speed  of  transmission  is 
encountered  in  the  recording  receivers,  particularly  in  the  EINTHOVEN 
galvanometer  (photographic)  method,  which  seems  to  have  responded 
to  the  highest  speeds f  used. 

*  On  airships,  aeroplanes,  etc.,  the  attendant  noises  make  telephone  reception 
very  difficult.  For  this  reason  the  coherer  has  been  returned  to  in  some  instances, 
in  conjunction  with  a  relay  controlling  the  circuit  of  a  small  incandescent  lamp. 
Relatively  short  and  longer  periods  of  incandescence  in  the  lamp  represent  dots  and 
dashes.278  However,  telephone  reception  has  also  been  used  with  considerable  suc- 
cess on  flying  machines. 

f  The  rapid  telegraph  apparatus  of  P.  O.  PEDERSEN,  operating  between  the 
POULSEN  stations  at  Lyngby  and  Esbjerg,  is  said  to  have  attained  a  speed  of  300 
words  per  min. ;  the  normal  speed  of  the  POULSEN  stations  is  given  as  150  words  per 
min.  (The  CULLERCOATS  station  transmits  200  words  per  min.  over  a  distance  of 
800  km.)  A  speed  of  100  words  per  min.  has  been  achieved  with  MARCONI  apparatus; 
the  transatlantic  MARCONI  stations  are  said  to  operate  at  "quelques  dizaines" 
words  per  minute. 


CHAPTER  XII 
RECEIVERS 

171.  The  Aerials  at  the  Receiving  Stations. — The  waves  sent  out  by  a 
transmitter  result  in  an  electromagnetic  alternating  field,  which  may  be  a 
rotating  field,  at  the  location  of  the  receiver.  Consequently  if  a  conduc- 
tor is  placed  within  this  field  oscillations  are  generated  in  it. 

The  conductor  for  this  purpose  is  the  antenna,  which  also  serves  for 
transmitting,  a  complete  station  being  equipped  for  both  sending  and 
receiving, 'just  as  in  ordinary  wire  telegraphy.  Usually  a  throw-over 
switch  is  provided  for  connecting  the  aerial  either  to  the  transmitter  or 
to  the  receiver,  as  may  be  desired ;  otherwise,  it  is  arranged  that  the  re- 
ceiver is  automatically  connected  to  the  aerial  whenever  the  station  is 
not  transmitting.280 

Following  a  suggestion  of  O.  SauiER,281  trees  have  been  successfully 
used  as  receiving  aerials  for  distances  of  about  50  km.  The  method  is  to 
hammer  a  nail  into  the  tree  a  few  yards  above  the  ground  and  to  connect 
the  receiving  apparatus  between  the  nail  and  the  ground. 


FIG.  365. 


FIG.  366. 


As  to  the  direction  of  the  aerial,  it  is  advantageous  to  have  this  the 
same  as  the  direction  in  which  the  electric  field  has  its  greatest  ampli- 
tude. This  depends  upon  the  ground  on  which  the  station  stands.  In 
the  one  limiting  case  (namely,  sea  water),  in  which  the  field  of  the  trans- 
mitted waves  is  a  vertical  alternating  field  (according  to  Art.  138),  a 
vertical  aerial  is  by  far  the  best.  In  the  other  limiting  case,  with  the 
station  standing  on  dry  ground,  the  direction  in  which  the  amplitude  of 
the  electric  field  is  a  maximum  is  apt  to  be  at  a  considerable  angle  to  the 
vertical  (Art.  139,  et  seq.) ;  hence  an  aerial  inclined  in  the  direction  shown 

303 


304  WIRELESS  TELEGRAPHY 

in  Fig.  365  (arrow  indicates  direction  of  wave  propagation)  is  materially 
more  efficient  than  a  vertical  aerial  or  one  inclined  as  that  of  Fig.  366.* 

172.  General  Consideration  of  the  Receiving  System.  —  a.  The  elec- 
tric field  surrounding  the  receiving  antenna  produces  an  e.m.f.,  8,  along 
its  length.  This  e.m.f.163 

8  =  E  .  a2h2  =  Eh'2  (1) 

where  E  is  the  component  of  the  transmitted  field  strength  in  the  direction 
of  the  aerial,  h2  the  total  and  h'2  the  effective  height  of  the  aerial,  a2  being 
its  form  factor  [Art.  lOOc]. 

Consequently  this  e.m.f.  for  a  given  field,  i.e.,  for  the  same  transmitter, 
increases  as  the  height  and  the  form  factor  of  the  antenna  are  increased. 
In  this  respect,  therefore,  great  height  and  large  form  factor  offer  the  same 
advantages  as  for  transmission;  moreover,  antennae  which  radiate  freely 
are  also  advantageous  for  reception  in  this  respect. 

b.  However,  from  another  standpoint  high  radiation  is  a  disadvantage 
for  reception;  for,  as  soon  as  the  receiving  antenna  begins  to  oscillate  it 
radiates  energy  at  a  rate  which  increases  as  the  radiation  resistance 
increases.  This  radiated  energy  is  lost  to  the  receiver,  which  can  make 
use  only  of  such  energy  as  is  carried  over  to  the  detector. 

The  conditions  282  existing  in  the  receiving  antenna  are  similar  to  those 
in  any  oscillator  acted  upon  by  an  external  e.m.f.  [Arts.  56  and  67].  If 
the  oscillator  is  tuned  to  the  frequency  of  the  external  e.m.f.  —  which  is  the 
only  case  we  need  consider  in  practice  —  it  will  oscillate  at  its  natural  fre- 
quency, the  amplitude  of  the  oscillations  growing  constantly  until  the 
point  is  reached  where  the  energy  consumed  in  the  receiver  during  one 
period  =  the  energy  supplied  to  it  by  the  external  e.m.f.  (the  transmitter) 
during  the  same  period.  Hence  the  maximum  amplitude  decreases  as 
the  energy  consumption  increases  and  therefore  also  as  the  radiation 
resistance  of  the  antenna  is  increased. 

With  undamped  oscillations  [Art.  676]  the  current  72  in  the  receiver  is 
given  by 


R2  being  the  total  resistance  of  the  receiving  antenna.  Consequently  the 
heat  developed  in  a  detector  of  resistance  R<j  (or  in  a  detector  circuit 
[Art.  175]  of  equivalent  resistance  Rd  [Art.  55c])  is 


z  eff    = 


r>,   \ 

it'*) 


*  Assuming  the  same  constants  as  those  on  which  Fig.  303  (page  254)  is  based, 
the  aerial  of  Fig.  365,  if  brought  to  a  vertical  position  would  reduce  the  amplitude 
by  18  per  cent,  and  if  brought  to  the  position  of  Fig.  366  would  cause  a  reduction  of 
about  66  per  cent,  (see  the  inclined  aerials  discussed  in  Art.  205). 


RECEIVERS  305 

(#'2  =  effective  resistance  of  the  antenna  without  the  detector).     If  the 
transmitted  oscillations  are  damped  (decrement  =  di)  it  follows  from 

r> 

Art.  70,  by  substituting  OAT2T    [Art.  Sd]  for  d2  therein,  that 

i__ .  JL        _!_      .  s  2 

R',Y    4N  ^      So 


Now  let  us  assume  that  the  receiving  antenna  is  so  well  constructed 
that  the  (JOULEAN)  heat  loss  in  its  wires  and  in  the  ground  is  negligible 
compared  to  the  radiation  losses.  Then  Rfz  =  R%. 

Moreover,  let  the  detector  resistance  be  at  its  best  value,  i.e.,  the  value 
at  which  the  heat  developed  within  the  detector  and  hence  also  the  range 
are  at  their  maximum.  With  undamped  oscillations  this  value  is  R'z; 
with  damped  oscillations  it  would  be  rR'z,  where  r  is  somewhere  between 
1  and  2  for  all  important  conditions  encountered  in  practice.  (If  the 
transmitting  and  receiving  antennae  as  well  as  the  ground  conditions  at 
both  points  are  the  same,  T  =  \/2  =  1.41.) 

Then  the  heat  developed,  Rdl<?eff,  with  undamped  oscillations  is 


and  with  damped  oscillations  is 

r      l     f        1 


Substituting  for  R?  its  value  from  Art.  lOOc  and  for  8  its  value  from 
equation  (1),  we  obtain  for  the  heat  developed  in  the  detector  with  un- 
damped oscillations, 

v  10io'X2  '  #o2c.g.s.  units, 
Xl 


and  with  damped  oscillations 


(1  -f  r)2     167T2  X  3  X  10-     <±  /          e*i- 

\  C?2> 

Accordingly  the  greatest  heat  development  attainable  in  the  detector 
is  entirely  independent  of  the  form  and  height  of  the  antenna  with 
undamped  oscillations  and  is  affected  only  very  slightly,  namely,  through 

the  value  ~r,  by  these  factors  in  the  case  of  damped  oscillations.     It  is 

increased,  however,  as  the  wave-length  of  the  oscillations  increases. 
20 


306  WIRELESS  TELEGRAPHY 

c.  Maximum  heat  development  in  the  detector  is  a  requirement  for 
obtaining  maximum  range.  The  resultant  increase  in  the  decrement 
of  the  receiver  may,  however,  be  undesirable  from  other  viewpoints 
(as  for  sharp  tuning).  Hence  the  energy  consumed  in  the  detector  is 
usually  left  considerably  below  the  possible  maximum. 

Assuming  it  to  be  so  low  that  Rd  <^  R?,  then  from  b  we  obtain  that  for 
undamped  oscillations 

Rdl^eff  =  rA  '  s°2  approximately 
K^ 

and  for  damped  oscillations 


or,  for  undamped  oscillations 

RJ^eff    =    2(167T2  X   1010)2  '    (W^T2   "   8°2  C-§'S*   UnltS 

and  for  damped  oscillations 

d  -  f-rs  •  EC?  c.g.s.  units. 


(167T2  xlO1")2     4  X  3  X 


/,    ,     A 
dl  I1  +  dj 


In  this  case  an  antenna  of  low  height  and  low  form  factor  is  at  a  great 
advantage  and  the  importance  of  long  wave-length  becomes  very  marked 

(R.  RUDENBERG163). 

d.  Nevertheless  we  must  remember  that  the  discussions  in  c  and  b 
take  only  incomplete  consideration  of  the  influence  of  the  wave-length, 
in  that  the  receiver  only  is  considered.  If  we  take  the  transmitter  into 
account  as  well,  the  conditions  become  altered. 

According  to  Art.  138c  and  the  second  foot-note  in  Art.  139c 


Substituting  this  value  in  the  equations  obtained  above,  the  heat  devel- 
opment in  the  case  of  maximum  range  (Rd  =  R%  and  Rd  =  fRz  resp.) 
becomes 


X1010 


for  undamped  oscillations,  and 


*  ai  =  form  factor  and  hi  =  height  of  transmitting  aerial;  ft  =  coeff.  of  absorp- 
tion [Art.  1396]  +  stray  field  coeff.  [Art.  1406];  /i0  =  current  amplitude  at  base  of 
transmitting  aerial. 


RECEIVERS  307 

for  damped  oscillations ;  while  in  the  case  of  the  best  possible  sharpness  of 
tuning  (Rd^  RZ)  these  values  become 


2 

4W        2       '      7    '      "          °      /1"2 


for  undamped  oscillations,  and 
3 


4X3X1010 


/,    ,    dA 
l  I1  +  dj 


for  damped  oscillations. 

In  the  first  case  (maximum  range)  long  wave-length  with  undamped 
oscillations  is  important  only  in  that  it  is  advantageous  in  regard  to 
absorption  [Art.  139/]  and  stray  field  [Art.  140]. 

In  the  second  case  (maximum  tuning  sharpness),  however,  long  wave- 
length offers  considerable  additional  advantages.  Moreover  in  this  case 
the  combination  of  a  freely  radiating  transmitting  aerial  with  a  weakly 
radiating  receiving  aerial  would  be  materially  superior  to  two  similar 
aerials. 

e.  According  to  d}  with  damped  oscillations  of  constant  frequency,  the 

current  effect  in  the  receiver  °c ^ — - —     The  current  effect  Ii2e//  a^ 

di  (1  +  -r ) 

\  «2/ 

I\  2 

the  base  of  the  transmitting  antenna  <*  — — -     Hence  the  current  effect  in 

the  receiver  °c e-L-r' 

,   »i 


It  follows  that,  in  making  long  distance  tests  "under  the  same  condi- 
tions," it  is  essential  that  not  only  the  current  effect  at  the  base  of  the 
transmitting  antenna  but  also  the  decrement  of  the  transmitter  oscil- 
lations remain  constant.  It  is  not  sufficient  to  simply  keep  the  current 
effect  at  the  base  of  the  transmitting  antenna  constant. 

1.  THE  ORIGINAL  MARCONI  RECEIVER 

173.  The  First  Arrangement. — a.  Fig.  367  shows  the  simple  arrange- 
ment used  by  MARCONI  in  his  first  experiments.  It  is  the  exact  counter- 
part of  the  original  transmitter  shown  in  Fig.  209,  the  spark  gap  of  which 
is  replaced  by  the  wave  indicator,  which,  in  the  original  MARCONI  equip- 
ment, was  a  metallic  granular  coherer. 

This  arrangement,  even  if  the  coherer  were  replaced  by,  say,  a  thermal 
detector  of  very  high  resistance,  would  have  the  great  disadvantage  of 
too  great  resistance  in  the  receiver  and  too  large  a  decrement  in  the 


308 


WIRELESS  TELEGRAPHY 


receiving  antenna.     If  the  equations  of  Art.  172  are  applied  to  this  case,* 
in  which  Rd  <  R'z,  we  obtain  approximately  for  undamped  oscillations: 


2Rd 


So' 


and  for  damped  oscillations 

RdPeff 


L.  J 

Rd    47V 


.         ..o, 

feo 


i.e.,  the  greater  the  resistance  of  the  detector,  the  less  heat  will  be  devel- 
oped in  it. 

Moreover,  to  the  high  resistance  of  the  metallic  granular  coherer, 
there  is  added  the  difficulty  that  when  unexcited  it  has  a  capacity  effect, 
while  when  excited,  it  is  simply  a  very  high  resistance. 
Hence  the  receiving  antenna  if  tuned  to  the  trans- 
mitter in  one  condition,  can  not  be  tuned  for  the  other. 
The  arrangement  of  Fig.  367  had  still  another 
\A  disadvantage:  It  was  easily  affected  by 
atmospheric  disturbances.  If  the  por- 
tion of  the  antenna  above  the  coherer, 
through  which  it  is  insulated  from 
ground,  obtained  only  a  slight  static 
charge,  this  brought  its  potential  differ- 
ence with  the  earth  sufficiently  high  to 
break  through  and  excite  the  coherer. 

174.  The  Marconi  Transformer. — 
This  last-mentioned  difficulty  was  what 
chiefly  induced  MARCONI  to  soon  remove 
the  coherer  from  the  aerial. 

He  replaced  it  with  a  coil,  Si,  and 
caused  the  latter  to  act  inductively  upon 
another  coil,  >S2,  having  a  much  greater 
QJ       number  of  turns  and  the  ends  of  which 
^ .—^JL.—^  wcre  connected  to  a  coherer  (Fig.  368).  f 

•  The  transformer  (SiSz)  thus  formed  by 

*  these  two  coils  was  called  the  <?  jigger." 

a.  Not  only  does  this   arrangement 


FIG.  367. 


FIG.  368. 


provide  a  direct  path  to  ground  for  static  charges  in  the  aerial,  but  the 
damping  of  the  antenna  retains  its  normal  value  and  is  not  appreciably 
altered  by  the  changes  in  the  coherer.  Consequently  the  oscillations  of 
the  antenna  may  rise  to  a  much  greater  amplitude.  When  the  coherer  is 
excited  by  the  oscillations  induced  in  $2,  a  closed  circuit  >S2/  is  formed. 
A  large  part  of  the  energy  in  the  antenna  is  then  transferred  to  this 

*  Assuming  that  natural  oscillations  of  the  antenna  are  still  possible, 
t  But  see  c  of  this  article. 


RECEIVERS 


309 


To  Relay 


FlG.   369. 


circuit  S2Jj  and  the  heat  thereby  developed  in  the  coherer  so  reduces 
the  latter's  resistance  that  the  relay  responds. 

b.  There  is  another  point  to  be  considered.  With  the  coherer  directly 
in  the  aerial,  the  use  of  multiple  antennae  gained  nothing  over  the  simple 
antenna.  The  use  of  several  wires  instead  of  a  single  aerial  wire  did  not 
increase  the  potential  across  the  coherer 
terminals,  and  the  greater  current  ampli- 
tude, obtainable  with  the  multiple  aerial, 
did  not  help  the  coherer  much.  Now, 
however,  it  became  possible  to  make  use 
of  the  increased  current  amplitude  of  the 
multiple  antenna,  for  with  the  transformer 
the  increased  current  could  be  used  to 
produce  much  higher  potentials  across 
the  coherer  than  would  be  obtained  in  the 
antenna  itself. 

To  be  sure,  these  advantages  can  only  be  secured  if  the  antenna  is 
tuned  to  the  transmitter  oscillations  and  the  secondary  circuit  ($2  + 
coherer  in  unexcited  condition*)  is  tuned  to  the  antenna.  The  impor- 
tance of  just  this  requirement  was  probably  not  recognized  at  the  time; 
however,  the  fact  that  the  entire  arrangement  operates  satisfactorily 

only  if  certain  requirements 
are  filled,  was  recognized  and 
pointed  out  by  MARCONI  from 
the  first.  The  requirements 
were  met  by  trying  out  in 
each  station  what  was  the  best 
form  of  the  transformer,  which 
as  a  matter  of  fact  consisted 
primarily  in  adjusting  the 
primary  and  secondary  fre- 
quencies (and  perhaps  also 
the  degree  of  coupling). 

c.  The  arrangement  of 
Fig.  368  can  not  be  used  j  ust 
as  shown  there;  for  the  coil 
$2  would  close  the  relay  circuit 
(see  Fig.  359)  even  when  the 
This  is  prevented  by  inserting 


FIG.  370. 


coherer  was  in  its  non-conducting  state. 
a  block  condenser,  C,  (Fig.  369  or  Fig.  370),  which  has  no  appreciable 
effect  upon  the  oscillations  if  its  capacity  is  sufficiently  great  [Arts.  30c 
and  41c]. 


The  latter  was  not  so  essential,  as  a  very  close  coupling  was  used. 


310 


WIRELESS  TELEGRAPHY 


2.  RECEIVERS  FOR  TUNED  TELEGRAPHY  WITH  DAMPED  OSCILLATIONS 

The  main  object  of  tuned  telegraphy  is  to  have  the  receiver  respond 
only  to  waves  of  a  certain  frequency  (wave-length)  and  not  at  all,  or  at  any 
rate  only  very  slightly,  to  waves  of  any  other  frequency  (wave-length).* 

The  solution  of  this  problem  varies  according  as  the  receiving  antenna 
is  highly  or  slightly  damped. 

175.  Receivers  for  Highly  Damped  Receiving  Antennae. — Such 
receivers  are  always  constructed  as  to  have  a  slightly  damped  secondary 
circuit  coupled  to  the  primary  (antenna)  circuit.  The  detector  may  be  in 
the  secondary  circuit  or  it  may  be  in  either  a  condenser  circuit  or  a  closed 
circuit  (detector  circuit)  coupled  to  the  secondary  circuit. 


To  Relay 


FIG.  371. 

All  these  circuits  are  tuned  to  the  transmitted  frequency  and  hence  are  in 
resonance  with  one  another. 

The  following  are  a  few  of  the  many  arrangements  which  are  or  have 
been  in  use,  many  of  them  being  very  similar  in  principle. 

a.  Condenser  Circuit  Secondary;  Inductive  Coupling  with  the  Aerial.— 
This  arrangement  was  used  by  MARCONI  and  with  it  he  first  demonstrated 
the  possibility  of  tuned  telegraphy,  f 

It  is  shown  diagrammatically  in  Fig.  371.     Condenser  C  serves  as  a 

*  This  condition  is  more  or  less  obtainable  by  simply  loosening  the  coupling  be- 
tween Si  and  £2  in  the  arrangements  of  Figs.  369  and  370  [see  Art.  ISOdJ;  in  fact 
these  connections  were  used  by  MARCONI  for  tuned  telegraphing. 

t  Probably  the  first  proposal  to  use  tuned  telegraphy  was  that  of  O.  LODGE  (Brit. 
Patent  11575  of  1897,  applied  for  May  10,  1897).  In  this  patent  some  of  the  re- 
quirements which  an  arrangement  for  tuned  telegraphy  must  fill  are  clearly  stated. 
LODGE,  however,  does  not  seem  to  have  had  any  practical  success  until  MARCONI 
completed  his  first  successful  experiments  in  tuned  telegraphy. 


RECEIVERS 


311 


block  condenser;  as  it  has  much  greater  capacity  than  condenser  Ci,  to 
whose  terminals  the  coherer  F  is  connected,  the  latter,  Ci  (in  conjunc- 
tion with  the  coherer  in  parallel)  determines  the  fundamental  frequency 
of  the  condenser  circuit  [Art.  46]. 


FIG.  372. 

Of  late,  the  MARCONI  Co.  makes  use  of  a  special  tertiary  circuit  for 
the  detector  in  its  commercial  stations.  This  so-called  "  multiple- 
tuning  apparatus"  of  the  MARCONI  Co.  is  shown  in  Fig.  372.*  The 
variable  condenser  at  the  upper  left  hand  and  the  self-induction  adjust- 
able in  steps  below  the  condenser,  §i 
serve  for  tuning  the  aerial.  The 
variable  condenser  in  the  middle  is 
part  of  the  secondary  or  intermediate 
circuit,  while  that  at  the  upper  right 
belongs  to  the  detector  circuit.  The 
self-induction  of  these  two  (secondary 
and  tertiary)  circuits  is  adjusted  to 
the  same  step  in  both  simultaneously. 

b.  Condenser  Circuit  Secondary, 
Direct  Coupling  between  Aerial  and 
Condenser  Circuit. — This  arrangement 
was  used  by  LODGE  and  MuiRHEAD283 
with  the  granular  coherer  and  by  the 
TELEFUNKEN  Co.  (see  diagram  of 
connections,  Fig.  373)  with  the 
SCHLOMILCH  detector,  when  particularly  sharp  tuning  was  desired. 

The  TELEFUNKEN  Co.  used  a  special  tertiary  condenser  circuit 
(777,  Fig.  373),  as  proposed  by  F.  BRAUN,284  containing  the  effective 
condenser  C2  and  the  block  condenser  of  large  capacity,  C. 

*  Courtesy  of  the  MARCONI  Co. 


To  Relay 


FIG.  373. 


312 


WIRELESS  TELEGRAPHY 


Fig.  374  illustrates  a  TELEFUNKEN  receiver  for  thermal  detectors  on 
this  same  principle.  The  primary  inductance  (7  +  77  in  Fig.  373)  is 
divided  into  two  parts.  One  part  (marked  "4"  in  Fig.  374)  is  coupled 
to  the  condenser  circuit  777  (Fig.  373)  containing  the  detector,  while  the 
other  part  (at  the  upper  right  hand  in  Fig.  374  and  marked  "EA")  con- 


FIG.  374. 

sists  of  a  coil  of  variable  self-induction  (RENDAHL  variometer).  The 
condensers  (P,  Fig.  374  =  Ci,  Fig.  373  and  S,  Fig.  374  =  Ca,  Fig.  373) 
are  variable  plate  condensers. 

The  results  obtained  with  the  connections  shown  in  Fig.  373  depend 
very  largely  on  the  relative  amount  of  self-induction  in  7  and  77  as  com- 


RECEIVERS 


313 


pared  with  the  effective  self-induction  of  the  rest  of  the  antenna  and  of 
the  " lengthening "  or  " loading"  coils  in  it.  If  the  self-induction  of  / 
and  II  is  relatively  small,  as  was  the  case  in  what  has  just  preceded,  the 
primary  circuit  must  be  considered  as:  Aerial,  coils  I  and  //,  ground; 
while  the  secondary  would  be  comprised  of  the  condenser  circuit  Ci, 
coil  I  +  //.  But  if  the  self-induction  of  coils  /  and  II  is  relatively 
large,  we  have  a  case  of  the  "fly-wheel"  system,  described  in  Art.  986, 
applied  to  the  receiver.  The  primary  circuit  then  consists  of  the  con- 
denser circuit  comprised  by  the  inductance  I  +  //  (Fig.  373)  and  the 
capacity  formed  by  the  condenser  Ci  in  parallel  with  the  capacity  an- 
tenna-ground. 

c.  Single  Coil  Secondary. — With  this  arrangement,  in  which  the  natural 
oscillations  of  coils  [Art.  23]  and  not  of  condenser  circuits  is  employed, 
A.  SLABY  and  COUNT  ARCO,  following  soon  after  MARCONI,  succeeded  in 
obtaining  a  tuned  radio-telegraph  system.  It  is  now  no  longer  in  use. 

176.  Receivers  for  Weakly  Damped  Antennae. — If  the  decrement 
of  the  antenna  is  not  much  different  from  that  of  a  well  designed  con- 


FIG.  375. 


FIG.  376. 


77777/777T/ 

FIG.  377. 


denser  circuit  without  spark  gap,  then  the  use  of  a  condenser  circuit  as 
secondary  no  longer  offers  the  same  advantages  as  with  a  strongly  damped 
antenna  [Art.  180d]. 

Hence,  in  this  case,  which  applies  to  all  quenched  spark  operation,  the 
antenna  is  coupled  to  a  closed  detector  circuit285  containing  the  detector 
as  shown  in  Fig.  375.*  The  coupling  may  be  either  inductive  (Fig.  375) 
or  conductive  (Fig.  378). 

The  TELEFUNKEN  Co.160  has  applied  this  method  of  connection  for 
use  with  transmitters  arranged  for  two  standard  wave-lengths  in  the 
following  manner.  An  inductance  Si  (Figs.  376  and  377)  is  always  left 
in  the  receiving  antenna,  in  which  there  is  also  a  condenser  C.  When  the 
transmitter  is  working  on  the  short  wave,  Si  and  C  are  placed  in  series 
(Fig.  376),  while  for  the  longer  wave  they  are  connected  in  parallel 
(Fig.  377).  In  the  latter  case  we  again  have  the  "fly-wheel"  connection 

*  C'  is  simply  a  block  condenser  of  great  capacity. 


314  WIRELESS  TELEGRAPHY 

[Art.  986].  A  receiver  built  on  this  principle  is  shown  in  Fig.  236  (marked 
"33");  C  is  a  variable  plate  condenser  by  means  of  which  the  receiving 
antenna  can  always  be  exactly  tuned  to  the  transmitted  oscillations. 

177.  Tuning  the  Receiver  for  a  Double  Wave  Transmitter. — In  Arts. 
175  and  176  it  was  tacitly  assumed  that  the  transmitter  furnished  a  wave 
of  only  one  length.     This  is  the  case  with  the  WIEN  transmitter,  but  is 
true  of  the  BRATJN  transmitter  only  if  the  coupling  between  the  primary 
and  secondary  circuits  is  very  loose. 

If  the  coupling  in  the  BRAUN  transmitter  is  not  very  loose,  two  waves 
of  different  length  are  obtained.  The  question  then  at  once  suggests 
itself:  Which  wave  shall  the  receiver  be  tuned  for?285a 

This  question  is  justified  from  two  standpoints,  viz.: 

a.  There  is,  firstly,  the  question  per  se  as  to  whether  it  is  better  to 
tune  the  receiver  for  the  longer  or  for  the  shorter  wave.  In  Art.  106a, 
the  reasons  in  favor  of  the  shorter  wave-length  (higher  frequency)  were 
discussed.  On  the  other  hand,  the  fact  remains  that  the  shorter  wave  is 
more  rapidly  absorbed  in  the  daytime  than  the  longer  wave  [Art.139/] 
and  that,  moreover,  the  longer  wave  is  more  efficient  in  regard  to  produc- 
ing useful  energy  consumption  in  the  receiver  [Art.  1726].  As  a  matter 
of  fact,  however,  it  is  universal  practice  to  tune  for  the  shorter  wave,  so  far 
as  the  author  knows. 

6.  Secondly,  there  may  be  some  question  whether  it  is  best  to  have 
the  receiver  tuned  exactly  for  the  wave-length  to  which  it  should  respond. 

If  the  receiver  consisted  of  a  single,  slightly  damped  system,  then 
[see  Art.  87a]  a  certain  definite  small  displacement  from  exact  resonance 
(i.e.,  a  slight  dissonance)  between  the  receiver  and  the  transmitter  oscil- 
lations should  give  the  best  results,  at  least  in  case  the  transmitter  is 
quite  loosely  coupled  so  that  its  two  waves  are  nearly  of  the  same  fre- 
quency. Even  if  the  receiver  consists,  not  of  a  single,  but  of  two  or  three 
loosely  coupled  circuits  or  systems,  it  is  very  probable  that  the  same  holds 
true.  Accordingly,  it  is  not  unreasonable  that,  with  a  not  very  closely 
coupled  transmitter  a  slight  displacement  from  resonance  may  be  ad- 
vantageous, or,  to  put  it  more  correctly,  that  well  adjusted  receiving 
stations  really  operate  at  a  point  slightly  off  exact  resonance. 

178.  Adjustment  of  the  Energy  Delivered  to  the  Receiver. — Accord- 
ing to  Art.  172,  it  is  of  great  importance  for  the  heat  developed  in  the 
wave  indicator  and  hence  for  the  range  of  operation,  that  the  energy 
delivered  to  the  wave  indicator  has  a  distinct  relation  to  the  energy 
losses  in  the  receiver.     On  the  other  hand,  maximum  sharpness  in  tuning 
[Art.   180]  requires  the  lowest  possible  damping  and  hence  minimum 
energy  delivered  to  the  wave  indicator.     Therefore,  either  one  or  the 
other  requirement  will  be  met  according  as  the  chief  object  in  view  is 
longer  range  or  very  sharp  tuning.     Or,  otherwise,  a  compromise  is  made, 
the  energy  supply  to  the  wave  indicator  being  adjusted  to  give  a  good 


RECEIVERS 


315 


range,  without  allowing  the  sharpness  of  tuning  to  fall  below  the  desired 
practical  limit. 

The  amount  of  energy  delivered  to  the  wave  indicator  is  adjusted  by 
varying  the  degree  of  coupling  between  the  detector  circuit  and  the  antenna  or 
the  secondary  circuit  of  the  receiver. 

Figs.  378  and  379*  show  the  method  of  arranging  a  conductive  coup- 
ling of  the  detector  circuit f  direct  with  the  antenna  in  Fig.  378  and  with 
the  secondary  circuit,  ABCi,  of  the  receiver  in  Fig.  379.  The  coupling 
is  varied  by  means  of  the  sliding  contact  Sc.  As  the  portion-  A-Sc  of 


C      Telephone 


FIG.  378. 


FIG.  379. 


the  coil  AB  is  increased  (or  decreased),  the  current  flowing  through  the 
detector  Z  and  hence  the  action  in  the  detector  is  increased  (or  decreased) 
while  the  damping  is  also  increased  (or  decreased). 

For  inductive  coupling  of  the  detector  circuit,  the  arrangements  shown 
in  Figs.  375-377  can  be  used  if  the  coupling  between  Si  and  S2  is  variable 
[Art.  54]. 

179.  Receivers  for  Two  Different  Detectors. — In  receiving  stations 
where  two  different  wave  indicators  (say,  one  for  telephone  reception,  the 
other  for  call  signaling  or  for  recording)  are  to  be  used,  it  usually  does  not 
suffice  to  simply  install  a  throw-over  switch  for  connecting  either  wave 
indicator  to  the  rest  of  the  apparatus.  Aside  from  the  fact  that  this 
would  limit  the  reception  to  one  of  the  wave  indicators  at  a  time,  it  is 
advisable  to  have  separate  secondary  circuits  adapted  to  the  individual 
requirements  of  each  indicator. 

*  This  arrangement  of  circuits  may  be  considered  as  dividing  the  current  between 
the  two  parallel  branches  consisting  of  the  self-induction  A-Sc  and  the  detector  Z 
with  its  block  condenser,  C. 

f  These  connections  were  used  by  the  TELEFUNKEN  Co.,  in  conjunction  with  the 
electrolytic  detector. 


316 


WIRELESS  TELEGRAPHY 


Recording 


The  arrangement  used  by  the  TELEFUNKEN  Co.  for  this  purpose  and 
illustrated  in  Fig.  380  will  serve  as  an  example.  It  requires  little  or  no 
further  explanation;  the  "tuning  coil"  and  the  variable  condenser  C 
serve  for  tuning  the  aerial.  Fig.  381 82  shows  the  construction  of  the  tun- 
ing coil,  Figs.  38282  and  38382  are  the  coupling  transformers  for  the  record- 
ing and  for  the  telephone  re- 
ceivers respectively,  arranged  for 
adjustable  coupling.  Fig.  384 
shows  the  entire  outfit  assembled 
as  a  unit. 

180.  The  Sharpness  of  Tun- 
ing.— If  the  frequency  of  the 
transmitter  is  changed,  the  effect 
upon  the  receiver  will  also 
change.  Assume  that  a  thermal 
wave  indicator  (e.g.,  a  thermo- 
couple) is  used  in  the  receiver. 
Plot  the  deflections  of  the  gal- 
vanometer in  the  circuit,  which 
deflections  are  proportional  to 


=_ ~\  To  Telephone 


_~}  To  Relay 


FlG.   380. 


FIG.  381. 


the  current  effect  in  the  detector,  as  ordinates  and  the  different  trans- 
mitter frequencies  as  abscissae.  The  resulting  "resonance  curve  of  the 
receiver"  will  be  of  the  form  of  the  heavier  curve  in  Fig.  385;  the 
effect  is  a  maximum  at  a  certain  transmitter  frequency,  No,  at  which 
frequency  the  transmitter  is  said  to  be  "in  tune,"  while  at  any  other 
frequency  it  is  "out  of  tune." 

If  now  the  galvanometer  is  replaced  by  a  relay,  the  latter  will  not 
respond  below  a  certain  current.  Thus,  let  us  assume  that  under  the 
conditions  represented  by  the  heavy  curve  in  Fig.  385,  the  current 
at  resonance  is  }{Q  milliampere  and  that  at  least  %Q  milliampere  is 
required  to  actuate  the  relay;  then  the  relay  will  not  respond  at 
frequencies  below  0.967  NQ  or  above  1.033  jV0,  i.e.,  at  a  dissonance  of 
more  than  3.3  per  cent,  in  the  transmitter.  This  3.3  per  cent,  is 


RECEIVERS 


317 


FIG.  382. 


FIG.  383. 


FIG.  384, 


318 


WIRELESS  TELEGRAPHY 


sometimes  called  the  "necessary  dissonance".     Apparently,  therefore, 
the  "sharpness  of  tuning"  varies  inversely  as  the  necessary  dissonance.* 

a.  The  sharpness  of  tuning  depends  upon  two  factors,  viz. : 

1.  The  shape  of  the  resonance  curve  (Fig.  385)  and  hence  upon  the 
sharpness  of  resonance  [Art.  70c]. 

2.  The  factor  of  safety  [Art.  148]  of  the  station. 

The  relation  to  the  form  of  the  resonance  curve  is  evident  from  Fig. 
385.  The  steeper  the  curve,  the  sharper  is  the  resonance,  and  hence  the 
sharper  will  be  the  tuning.  Thus,  if,  e.g.,  the  resonance  curve  were  the 
flatter,  light  curve  in  Fig.  385,  then,  under  the  same  conditions  as  were 


0.9  N0 

\    ,    , 


1.1  N0 

_\ 


Dissonance  in 


-10  98765432  1012345G7S  9  10 

FIG.  385. 


assumed  previously,  the  necessary  dissonance  would  be  about  6.5  per 
cent.,  the  sharpness  of  tuning  correspondingly  less. 

As  to  the  other  factor  which  determines  the  sharpness  of  tuning,  it  was 
pointed  out  above  that  under  the  conditions  assumed  J^o  milliampere  was 
required  to  make  the  relay  respond.  When  the  station  is  tuned,  i.e., 
under  normal  operating  conditions  y±Q  milliampere  is  supplied  to  the  re- 
lay. Hence  the  station  has  a  working  factor  of  safety  of  \/3«  H  the 
working  safety  factor  were  lower,  e.g.,  \/1.5;  then  under  the  conditions 
represented  by  the  heavy  line  curve  of  Fig.  385  the  relay  would  only  re- 
spond within  2  per  cent,  of  resonance,  so  that  the  tuning  would  be  much 
sharper. 

From  the  preceding  it  is  evident  that  record  tests  giving  very  great 
sharpness  of  tuning  must  not  be  considered  as  conclusive.  By  ad- 
justing a  receiver  so  that  the  slightest  deviation  from  resonance  suffices 
to  prevent  the  apparatus  from  responding  as  an  indicator,  the  tuning 
appears  to  be,  in  fact  really  is,  very  sharp;  but  the  station  is  entirely  unfit 
for  normal 


service. 


*  The  best  measure  of  the  sharpness  of  tuning  is  the  reciprocal  of  the  necessary 
dissonance  value. 


RECEIVERS 


319 


&.  As  to  the  form  of  the  resonance  curve,  this  is  easily  determined  for  a 
receiver  without  secondary  condenser  circuit  as  used  for  weakly  damped 
antenna  oscillations.  For  if  the  conditions  in  the  detector  circuit  are  such 
that  the  current  effect  in  it  is  proportional  to  that  in  the  antenna  [Art. 
556],  then  the  resonance  curve  is  exactly  the  same  as  that  corresponding  to 
a  primary  circuit  of  decremented  in  the  transmitter  and  a  decrement  dz  in 
the  receiving  antenna  and  is  determined  by  the  sum  of  the  decrements 
of  the  transmitting  and  receiving  antennae.  At  the  same  time,  the  decre- 
ment of  the  receiving  antenna  of  course  depends  also  upon  the  amount  of 
energy  supplied  to  the  detector. 

The  resonance  sharpness  and,  hence,  also  the  sharpness  of  tuning  in- 
crease as  the  damping  of  the  transmitter  oscillations  and  that  of  the  re- 
ceiving antenna  decrease. 

c.  The  resonance  curve  for  receivers  with  secondary  condenser  circuit 
is  easily  calculated  if  the  transmitter  oscillations  are  undamped  and  if  the 
primary  and  secondary  circuits  of  the  receiver  are  very  loosely  coupled. 
In  this  case,  in  a  very  short  space  of  time  only  the  impressed  undamped 


0,8 
0.7 
0.6 
0.5 
0.4 

'  0.3 
0.2 

'0.1 


/I 


7- 


\ 


\ 


\ 


1.005         1.010         1.015        1.020 


0.980    ,       0.985          0.99  0.995  1 

N/Nt~* 

FIG.  386. 

oscillations  of  the  transmitter  frequency  exist  in  both  primary  and  sec- 
ondary circuits  of  the  receiver,  and  they  almost  solely  determine  the 
current  effect  [Art.  696].  A  simple  consideration  of  this  shows  that  the 
resonance  curve  of  the  receiver  is  obtained  approximately*  in  the  following 
manner.  Plot  the  resonance  curve  (the  thin  full  line  curve  in  Fig.  386) , 
which,  according  to  the  second  foot-note  of  Art.  74a,  corresponds  to  the 

*  The  exact  equation  for  the  resonance  curve  is : 


tor 


A/I  + 


320 


WIRELESS  TELEGRAPHY 


decrement  of  the  receiving  antenna  with  undamped  oscillations  (di  =  0), 
the  ordinates  being  the  values  of  I2eff/I2r  effm  Similarly,  plot  the  resonance 
curve  corresponding  to  the  decrement  of  the  secondary  circuit  of  the 
receiver  (dashed  line  in  Fig.  386).  Then  find  the  product  of  the  ordinates 
of  these  two  curves  corresponding  to  the  same  abscissa.  This  product  is 
approximately*  the  value  of  the  ordinate  of  the  desired  resonance  curve 
(heavy  full  line  curve  in  Fig.  386)  at  the  same  abscissa. 

In  Fig.  386,  d2l  (receiving  antenna)  =0.1,  d2z  (secondary  circuit  of 
receiver)  =  0.05.  For  d^  =  0.02  the  dash-and-dotted  line  is  obtained.* 

From  the  preceding,  it  follows  that  by  the  use  of  a  secondary  circuit  a 
much  sharper  tuning  is  possible  than  without  a  secondary,  the  difference 
being  the  more  marked  the  less  damped  the  secondary  circuit  is. 

d.  If  the  transmitter  oscillations  are  damped,  the  conditions  governing 
a  receiver  with  secondary  condenser  circuit  are  quite  different.  In  general 
two  oscillations  (of  different  frequency)  are  induced  in  the  receiving 
antenna,  one,  the  impressed  oscillation,  of  the  same  frequency  and  dec- 
rement as  the  transmitter  oscillation,  the  other  the  natural  oscillation  of 
the  fundamental  frequency  and  decrement  of  the  receiving  antenna  and 
hence  of  the  same  frequency  as  the  secondary  circuit  which  is  tuned  to  the 
receiving  antenna.  Consequently,  even  if  the  impressed  oscillations  have 
but  little  effect  upon  the  secondary  circuit,  the  natural  oscillations  of  the 
receiving  antenna  will. 


1 

O.'J 
0.8 
0.7 
0.6 
0.5 


X 


, 


5  4  S  2  1  0  1  2  34  5 

Dissonance  — >• 

FIG.  387. 

The  conditions  encountered  here  are  relatively  complicated,  as  three 
damped  systems  (transmitter  oscillations,  primary  circuit  and  secondary 
circuit  of  receiver)  come  into  question,  and  moreover  as  two  quite  different 
requirements,  viz.,  maximum  resonance  and  sharpness  of  tuning  on  one 
hand,  maximum  range  on  the  other  hand,  counteract  each  other  in  this 
case. 


*  See  foot-note  on  preceding  page. 


RECEIVERS 


321 


So  far  as  the  resonance  sharpness  is  concerned,  we  may  assume  that, 
other  things  being  equal  (equal  decrements),  it  increases  the  looser  the 
coupling  between  antenna  and  secondary  circuit  of  the  receiver  is  made. 
The  ideal  case,  therefore,  is  that  of  extremely  loose  coupling.  This  has 
been  theoretically  investigated  by  H.  RiEGGER;286  some  of  his  results  are 
shown  in  Figs.  387*  and  388A  and  B.* 

The  conditions  assumed  for  Fig.  387  are  about  those  existing  in  the 
BRAUN  transmitter  with  greatly  damped  antenna;  decrement  di  of  the 
exciting  circuit  in  the  transmitter  and  hence  the  decrement  of  the  trans- 
mitted oscillations  =  0.1  approximately;  decrement  J2l  of  the  receiving 
antenna  =  0.3;  decrement  d^  of  the  condenser  circuit  in  the  receiver  = 


0.9 
0.8 
0.7 
0.6 
0.5 

\M 

0.3 


0.1 


«\ 


i          o         i 

Dissonance  — 

FIG.  388A. 


0.03.  The  resonance  curve  (a)  of  the  current  effect  in  the  condenser  cir- 
cuit shows  that  the  sharpness  of  resonance  which  can  be  attained  (p  =  50 
approx.  [Art.  70c])  is  considerably  greater  than  it  would  be  without 
a  secondary  condenser  circuit,  with  the  antenna  acting  directly  upon 
the  detector.  In  this  latter  case  the  resonance  curve  would  be  as  shown 
by  curve  b,  the  resonance  sharpness  would  =  15.7,  corresponding  to 
di  +  d2l  =  0.4. 

The  assumptions  on  which  Figs.  388A  and  3885  are  based  correspond 
to  a  quenched  gap  transmitter  and  two  antennae  with  greatly  reduced  radia- 
tion damping:  di  =  d2l  =  0.03.  In  Fig.  388A  a  relatively  large  amount 
of  energy  supplied  to  the  detector  by  the  condenser  circuit  (d22  =  0.03) 
is  assumed,  while  in  Fig.  3885,  this  is  assumed  to  be  very  low  (d^  =  0.01). 
As  a  means  of  comparison,  the  curve  b,  the  resonance  curve  which  would 
be  obtained  in  the  receiver  without  a  secondary  condenser  circuit  and  cor- 
responding to  di  +  d2l  =  0.06,  p  =  105,  has  been  drawn  in  each  figure. 
Here  again  it  is  seen  that  the  secondary  condenser  circuit  considerably 

*  In  these  figures  curve  c  is  the  resonance  curve  for  d\  +  d22;  it  almost  coincides 
with  curve  a. 
21 


322 


WIRELESS  TELEGRAPHY 


increases  the  resonance  sharpness  (p  =  143  in  Fig.  388A,  p  =  156  in  Fig. 
3885). 

Accordingly  the  use  of  a  secondary  condenser  circuit  even  in  con- 
junction with  very  slightly  damped  antennae,  is  justified  when  particularly 
sharp  tuning  is  desired.287  On  the  other  hand,  however,  the  examples 
illustrated  show  that  the  resonance  sharpness  attainable  without  a  sec- 
ondary condenser  circuit,  suffices  for  all  practical  purposes  and  in  fact 
would  suffice  even  if  the  decrements  of  the  antennae  were  double  the 
decrements  assumed  for  Figs.  388A  and  B. 

The  range  is  determined  on  one  hand  by  the  energy  supplied  to  the 
detector  (and  hence  by  the  damping,  d?2,  of  the  secondary  condenser  cir- 


0.1 


V-& 


54  2  21  012  345$ 

Dissonance  — >• 

FIG.  3885. 

cuit)  and  on  the  other  hand  by  the  degree  of  coupling  between  the  re- 
ceiving antenna  and  the  secondary  condenser  circuit.  The  practical 
problem  therefore  is :  how  far  may  or  must  we  go  with  both  these  factors 
to  obtain  maximum  range  without  seriously  reducing  the  sharpness  of  tun- 
ing?* Such  investigations288  as  have  been  made  to  date  do  not  suffice  for 
arriving  at  a  general  answer  to  this  question.  Actual  experience  in  prac- 
tice has  shown  that  in  those  cases  where  there  is  any  condenser  circuit  in 
the  receiver,  the  coupling  between  condenser  circuit  and  receiving  antenna 
must  in  any  case  be  very  loose,  if  good  tuning  is  at  all  required. f  It  has 
further  been  shown  that  this  loose  coupling  may  be  adopted  without  mate- 

*  A  comparison  of  the  two  curves  marked  "a"  in  Figs.  388A  and  B  respectively,  is 
instructive  in  this  connection.  The  sharpness  of  resonance  is  almost  the  same  in 
both  cases  although  the  energy  supplied  to  the  detector  in  Fig.  388A  was  assumed 
about  three  times  as  great  as  that  in  Fig.  3885. 

t  Recognition  of  this  requirement  originated  in  the  theoretical  investigations  of 
M.  WiEN289  and  in  the  experiments  made  by  H.  BRANDES  and  L.  MANDELSTAM289  at 
almost  the  same  time.  Close  coupling  is  used  almost  solely  for  such  cases  where 
sharp  tuning  is  of  no  importance  and  where  it  is  desired  to  communicate  with  various 
stations  of  somewhat  different  wave-length,  as  for  instance  in  coastal  stations  com- 
municating with  ships  at  sea  or  again  where  it  is  desired  to  "listen  in"  to  traffic 
between  other  stations  [see  Art.  184aj. 


RECEIVERS  323 

rially  sacrificing  range,  as  long  as  the  transmitter  oscillations  are  not  too 
strongly  damped.  The  reason  for  this  is  that  conditions  in  the  loosely 
coupled  system  (secondary  or  tertiary  circuit  of  the  receiver)  which  acts 
directly  upon  the  wave  indicator,  are  about  of  the  nature  described  in 
Art.  61  c  —  more  and  more  energy  accumulates  in  this  system  during  a 
series  of  periods  or  cycles,  so  that  eventually  quite  a  large  amount  of 
energy  exists  in  the  system,  even  if  only  very  little  is  transferred  to  it  in 
each  period. 

This,  however,  is  based  on  the  assumption  that  all  energy  consumed  in 
the  secondary  circuit  (JOULEAN  heat,  eddy  currents)  without  being  useful 
in  the  wave  indicator,  is  kept  as  small  as  possible.  Otherwise,  the  use 
of  a  secondary  circuit  in  the  receiver  may  be  detrimental  to  the  range 
without  being  of  much  value  toward  sharpness  of  tuning. 

It  may  therefore  be  important  to  block  the  path  of  the  oscillations  into 
the  circuits  of  the  auxiliary  apparatus  where  a  part  of  their  energy  would 
be  wasted,  by  means  of  choke  coils  [Art.  1656].  If  this  is  done,  however,  it 
is  essential  that  the  choke  coils  themselves  do  not  consume  any  energy;* 
hence  they  must  have  no  iron  cores.  With  iron  cores,  they  would  serve 
their  purpose  of  keeping  the  oscillations  out  of  the  auxiliary  apparatus 
fully  as  well  if  not  even  better,  but  hysteresis  and  eddy  current  losses  in  the 
cores  would  result. 

181.  R.  A.  Fessenden's  Method  for  Maintaining  Secrecy  of  Tele- 
grams.290 —  The  "secrecy  sender"  of  Fig.  389  transmits  waves  uninterrupt- 
edly, but  when  the  circuit  of  the  wire  loop,  K,  is  closed,  their  wave-length, 
X',  differs  from  X,  the  wave-length  to  which  the  receiver  is  tuned,  by  an 
amount  given  by  FESSENDEN  as  Y±  per  cent.  If  the  circuit  of  this  wire 
loop  is  broken  by  pressing  the  keyf  the  transmitter  oscillations  have  the 
wave-length,  X,  for  which  the  receiver  is  tuned.  { 

At  the  receiver  ("interference  preventer")  (Fig.  390)  the  oscillations 


in  the  aerial  branch  off  between  two  paths,  ACiSiE  and  ACzS^E.  The 
former  is  tuned  to  the  wave-length  X,  the  latter  being  so  dimensioned  that 
with  the  wave-length  X'  the  amplitude  of  the  oscillations  in  C2S2  becomes 
equal  to  that  in  CiSi*  The  coils  S\  and  S'%,  which  are  coupled  with  Si 
and  $2  respectively,  are  wound  so  as  to  oppose  or  "buck"  each  other,  so 
that  with  wave-length  X'  the  electromotive  forces  induced  in  S\  and  $'2, 
practically  neutralize  each  other. 

Hence,  if  the  transmitter  is  operated  without  depressing  the  key  in 
loop  K  (Fig.  389)  and  wave  X'  is  sent  out,  no  appreciable  oscillations  are 
induced  in  the  circuit  CS'zDS'i  of  the  receiver.  But  if  the  key  in  loop  K 

*  The  construction  of  really  good  choke  coils  is  not  so  very  simple  a  matter. 
Accordingly  systems  or  methods  of  connection  in  which  no  choke  coils  are  needed 
offer  a  practical  advantage. 

t  The  key  is  not  drawn  correctly  in  Fig.  389. 

t  Compare  P.  O.  PEDERSEN'S  method  for  undamped  oscillations  [Art.  127  c]. 


324 


WIRELESS  TELEGRAPHY 


is  closed  and  wave  X  is  sent  out,  oscillations  of  very  high  amplitude  are 
obtained  in  branch  CiSi  and  of  very  low  amplitude  in  C2$2;  consequently 
the  electromotive  forces  induced  in  S'i  and  S'z  do  not  neutralize  each 
other,  and  the  wave  indicator,  D,  responds  accordingly. 

Undoubtedly  this  method  makes  the  reception  of  telegrams  very  diffi- 
cult. Unless  the  receiving  station  is  tuned  exactly  for  the  wave-length  X 
and  so  sharply  that  a  dissonance  of  %  per  cent,  suffices  to  make  the  sig- 
nals disappear,  the  signals  will  be  received  constantly,  whether  the  key  at 
the  transmitter  is  depressed  or  not. 


»f 
FIG.  390. 


The  practical  tests  conducted  by  the  NAT.  EL.  SIG.  Co.  with  this 
method  were  claimed  to  have  given  very  good  results,  even  in  overcoming 
atmospheric  disturbances  [Art.  183];  its  application,  however,  will  prob- 
ably remain  very  limited  to  a  few  special  cases. 

182.  Multiplex  Telegraphy. — The  solution  of  the  problem  of  construct- 
ing a  receiver  which  will  respond  within  certain  limits  only  to  a  single 
wave-length,  is  at  the  same  time  a  solution  of  the  problem  of  multiple 
telegraphy — receiving  telegrams  from  two  transmitters  simultaneously 
on  one  antenna. 

a.  Fig.  391  illustrates  an  arrangement  of  this  kind  used  by  MARCONI 
with  considerable  success.  For  the  longer  wave,  the  primary  circuit 
consists  of  the  aerial,  coil  S,  primary  coil  I  of  the  transformer  and  ground. 
The  secondary  circuit  tuned  to  this  is  II.  For  the  shorter  wave,  the  pri- 
mary circuit  consists  of  the  aerial,  condenser  C,  primary  coil/' of  the  trans- 
former and  ground.  The  secondary  circuit  tuned  to  this  is  II' .  The 


RECEIVERS 


325 


conditions  are  such  that  the  system  to  the  right  does  not  respond  to  the 
longer  wave,  that  to  the  left,  not  to  the  shorter. 

Any  other  arrangement  for  tuned  telegraphy  can,  of  course,  be  simi- 
larly used  if  the  tuning  is  sufficiently  sharp.* 

b.  The  simultaneous  transmission  of  two  telegrams  from  the  same  an- 
tenna is  also  feasible.  It  is  simply  necessary  to  couple  two  different  con- 
denser circuits  with  the  aerial,  each  condenser  circuit  adjusted  so  as  to  be 


FIG.  391. 


in  resonance  with  its  own  secondary.  The  connections  used  by  MARCONI 
are  shown  in  Fig.  392;  as  in  Fig.  391,  the  portion  to  the  left  is  for  the 
longer  wave,  that  at  the  right,  for  the  shorter. 

c.  In  the  multiple  or  duplex  telegraph  systems  just  described  it  is 
essential  that  the  wave-lengths  of  the  two  transmitters  whose  telegrams 
are  to  be  received  on  the  same  antenna,  be  different.  Duplex  reception 
at  the  same  wave-length  is  possible  if  both  the  transmitters  are  tone  trans- 
mitters and  work  with  different  tones.  Tests  of  this  kind  have  been  made 
by  the  TELEFUNKEN  Co.;292  two  of  the  sound  intensifiers  described  in 

*  Thus  the  TELEFUNKEN  Co.,  e.g.,  has  received  telegrams  from  three  different 
stations  simultaneously  on  a  single  ship's  antenna.291 


326 


WIRELESS  TELEGRAPHY 


Art.  1666  were  connected  to  the  receiver,  each  adjusted  to  the  tone  of  one 
of  the  transmitters.  Perfect  duplex  reception  in  spite  of  equal  wave- 
lengths was  possible;  as  soon  as  the  two  tone  frequencies  differed  by  20 
per  cent. 

183.  Methods  for  Overcoming  Atmospheric  Disturbances. — a.  The 
atmospheric  disturbances  which  are  particularly  frequent  during  the  sum- 
mer months,  and  are  especially  noticeable  in  the  hours  from  noon  or  from 
sunset  to  sunrise,  even  in  stations  where  static  charging  of  the  antenna  is 


FIG.  392. 

out  of  the  question,  seem  to  originate  primarily  in  lightning  discharges 
between  two  clouds  or  between  a  cloud  and  the  earth.293  This  is  not 
contradicted  by  the  frequent  disturbances  experienced  under  a  clear  blue 
sky;  the  distance  over  which  clouds  can  be  seen  from  a  point  on  the  earth's 
surface  is  extremely  short  as  compared  to  the  distance  at  which  a  stroke 
of  lightning  can  excite  a  wave  detector.  Hence  an  electric  storm  makes 
itself  felt  in  a  radio-receiving  station  at  tremendous  distances. 

The  early  wireless  stations,  as  long  as  their  receivers  were  arranged  for 
relatively  highly  damped  waves  of  great  amplitude,  suffered  severely 
from  these  atmospheric  disturbances,  particularly  in  the  tropics.  Con- 
siderable improvement  resulted  as  soon  as  the  receivers  were  arranged 


RECEIVERS 


327 


FIG.  393. 


for  less  damped  transmitter  oscillations  of  lower  amplitude  (i.e.,  low  an- 
tenna decrement,  loose  coupling  with  the  secondary  condenser  circuit  or 
detector  circuit). 

Even  to-day  probably  the  best  protection  against  atmospheric  dis- 
turbances still  is  a  powerful  transmitter  permitting  ( 
the  use  of  very  loose  coupling  and  a  not  too  highly 
sensitive  wave  indicator  in  the  receiver. 

a.  MARCONI  has  devised  a  number  of  special 
arrangements  for  mitigating  the  effect  of  atmospheric 
disturbances.294 

1.  The  primary  circuit  of  the  receiver  consists  of 
the  aerial  and  PCE  (Fig.  393).  The  natural  oscilla- 
tions of  the  aerial  are  so  regulated*  by  means  of  coil 
S  and  condenser  C,  that  the  anti-node  of  current  and 
node  of  potential  occur  at  the  point  P  [see  Art.  31  et 
seq.].  Accordingly  if  waves  of  the  same  length  as  the 
natural  wave-length  of  the  antenna  strike  the  latter 
it  will  oscillate  with  a  potential  node  at  P.  If  now  a 
ground  connection  PE\  is  made  at  P,  no  appreciable 
current  will  flow  through  it. 

But,    if   any   other    electromagnetic    disturbance 

occurs,  the  greatest  part  of  the  current  induced  in  the  aerial  will  flow 
through  PEi  to  ground  as  its  impedance  is  lower  than  that  of  the  path 
~SCE.  Hence  the  effect  of  the  disturbance  upon  the  secondary  circuit 
(//)  is  greatly  diminished. 

Accounts  of  how  successful  this  arrangement  is  in  practicef  have  never 

been  published  so  far  as  the  author  is 
aware. 

2.  Another  method  of  the  MAR- 
CONI Co.  is  sketched  in  Fig.  394. 
Z>iZ>2  are  two  rectifying  detectors,  of 
opposite  polarity,  so  that  one  allows 
the  current  to  flow  through  it  in  one 
direction,  the  other  in  the  opposite 
direction  [Art.  162a].  For  one  of 
them,  let  us  say  Di,  the  size  of  the 
auxiliary  battery  (not  shown  in  Fig. 
394)  is  so  chosen  that  the  detector  is 
very  sensitive,  while  for  the  other,  Z)2, 
it  is  so  chosen  as  to  make  its  sensitiveness  very  low.  Consequently 
under  normal  operating  conditions  only  DI  responds  and  the  telephone 

*  The  aerial  is  of  course  also  tuned  to  the  transmitter. 

t  It  seems  probable  that  this  arrangement  would  also  be  effective  against  electro- 
magnetic waves  of  another  length,  hence  would  increase  the  sharpness  of  tuning. 


-    —D 


FIG.  394. 


328  WIRELESS  TELEGRAPHY 

receives  current  in  one  direction  only.  But  if  a  heavy  atmospheric  dis- 
turbance occurs,  both  detectors  respond,  the  current  flows  through  in 
both  directions  and  the  telephone  is  not  affected. 

b.  Those  radio-systems  which  produce  a  tone  of  more  or  less  purity  in 
the  receiving  telephone  have  proven  themselves  as  an  excellent  safeguard 
against  atmospheric  disturbances;  for  the  latter  are  heard  in  the  telephone 
as  short  dissonant  crackling  and  can  usually  be  easily  distinguished  from 
the  tone  signals. 

184.  Achievements  of  Tuned  Telegraphy. — The  advantages*  which 
make  tuned  telegraphy  so  decidedly  preferable,  are  best  expressed  as  the 
following  disadvantages  of  untuned  telegraphy: 

1.  The  telegrams  can  be  " picked  up"  by  any  and  all  stations  within 
the  range  of  the  transmitter :  no  secrecy  of  telegrams. 

2.  Communication  between  two  stations  A  and  B  can  be  crippled  by 
constantly  sending  out  signals  from  a  station  C  within  whose  range  A 
and  B  are  located:  deliberate  intentional  interference. 

3.  If  A  and  A'  on  one  hand  and  B  and  B'  on  the  other  hand  are  two 
sets  of  communicating  stations,  each  of  which  lies  in  the  range  of  the 
other  three  stations,  then  A  and  A'  can  not  communicate  while  B  and  Br 
are  exchanging  messages :  interference  between  stations. 

Whether  or  not  tuned  telegraphy  entirely  overcomes  these  obstacles 
can  not  be  stated  for  all  cases,  as  the  distance  between  the  stations  in 
question  and  their  ranges  are  very  important  factors.  The  question  can 
only  be:  To  what  extent  does  tuning  overcome  these  obstacles  and  are 
they  entirely  removed  in  any  specific  case? 

a.  As  regards  the  maintenance  of  secrecy  of  messages,  let  us  consider 
the  following  possible  case.  A  transmitting  station,  A,  and  a  receiving 
station,  A',  are  arranged  for  continuous  communication  with  each  other. 
Another  station,  C,  is  no  further  from  A  than  A'.  The  question  "  can  C 
be  prevented  from  receiving  telegrams  sent  out  from  A  by  means  of  the 
tuning  methods  previously  described?"  must  be  answered  by  a  decided 


"no." 


If  A  and  A'  are  arranged  for  constant  operation  their  actual  (ultimate) 
range  must  be  much  greater  than  the  distance  between  them  [Art.  148] 
and  the  wave  indicator  used  must  not  be  too  highly  sensitive.  It  follows 
that  it  will  then  be  possible  to  receive  the  telegrams  by  means  of  a  very 
sensitive  wave  indicator  in  an  untuned  closed  detector  circuit  [Art.  176]. 

In  general,  the  ordinary  receivers  will  serve  the  purpose  if  the  coupling 
is  made  closer.  Thus,  the  TELEFUNKEN  receiver  described  in  Art.  176and 
illustrated  in  Fig.  236  is  specially  arranged  for  this.  The  coil  correspond- 
ing to  S2  in  Figs.  376  and  377  is  movable  so  that  its  coupling  with  Si 
and  hence  also  the  coupling  between  the  antenna  and  the  detector  circuit 
can  be  varied.  In  order  to  tune  for  any  transmitter  which  is  sending  out 

*  Aside  from  the  increased  range  obtained  by  tuning. 


RECEIVERS  329 

signals  the  procedure  is  as  follows :  Starting  with  very  loose  coupling, 
gradually  make  the  coupling  closer  until  a  sound  is  heard  in  the  telephone. 
Then  adjust  the  condenser  until  the  sound  in  the  telephone  is  a  maximum. 
Finally  loosen  the  coupling  again  very  gradually,  readjusting  the  con- 
denser (C  in  Figs.  376  and  377)  if  this  is  necessary,  so  that  maximum 
loudness  is  obtained  in  every  case.295 

The  picking  up  of  messages  by  stations  other  than  those  intended  to 
receive  them,  is  made  more  difficult  according  as  the  amplitude  of  the 
oscillations  required  for  the  given  distance  is  reduced,  by  decreasing  the 
damping  of  the  oscillations. 

b.  Similarly  in  regard  to  intentional  interference,2950  assume  the  dis- 
turbing station  C  to  be  as  near  to  the  communicating  stations  AI  and  A2 
as  these  are  to  each  other  and  that  all  are  normal  types  of  stations  of 
moderate  ranges. 

First,  then,  we  must  take  for  granted  that  station  C  can  determine* 
the  wave-length  AI  and  A2  are  using  and  that  C  tunes  its  transmitter  to 
give  the  same  wave.  C  is  then  in  a  position  to  interfere  with  AI  and 
A2  even  if  its  range  is  only  one-half  or  one-third  of  that  of  AI  and  A2.f 

Eliminating  this  case,  however,  let  us  assume  that  C  is  unable  to 
determine  the  wave-length  used  by  AI  and  A*,  so  that  C's  wave-length 
differs  considerably  from  that  of  AI  and  A2.  Whether  or  not  C  can  inter- 
fere in  this  case  depends  simply  upon  how  far  it  can  raise  its  amplitude. 
If  the  receivers  at  AI  and  A2  have  very  loose  coupling,  C  would  not  be  able 


FIG.  395. 

to  reach  a  sufficiently  great  amplitude  in  its  transmitter  oscillations  to 
succeed  in  its  purpose.  {  Under  these  conditions,  therefore,  tuned  re- 
ceivers provide  a  much  greater  protection  against  intentional  interference. 

c.  In  regard  to  the  prevention  of  interference  between  a  number  of 
stations  in  the  same  general  vicinity,  let  us  consider  the  following  extreme 
case.  Assume  two  stations  AI  and  A2  very  close  together  at  one  place, 
BI  and  B2  similarly  located  at  another  place  (Fig.  395).  Then  we  must 
distinguish  clearly  between  the  following  two  cases: 

1.  The  two  stations  at  one  place,  say  AI  and  A2  operate  as  transmit- 
ters of  equal  strength,  while  those  of  the  other  place  BI  and  B2  are  both 
receivers  (Fig.  395).  Then,  by  suitable  tuning  methods,  it  can  un- 

*  Any  wave  meter  employing  a  wave  indicator  is  suitable  for  this  purpose.  Most 
wave  meters  are  arranged  so  as  to  be  suitable  for  measuring  waves  coming  in  from  a 
distance. 

t  In  view  of  the  safety  factor  with  which  AI  and  A2  must  operate  for  constant 
service. 

t  That  is,  -unless  C  could  come  very  near,  to  either  AI  or  A2. 


330  WIRELESS  TELEGRAPHY 

doubtedly  be  arranged  that  BI  receives  only  AI'S  telegrams  and  B2  only 
those  from  A 2,  even  if  the  frequencies  of  AI  and  A2  differ  by  only  a 
few  per  cent.  This  in  itself  constitutes  a  great  advantage  for  tuned 
telegraphy. 

2.  If,  however,  one  of  the  stations  must  receive  while  its  neighbor  is 
transmitting,  the  conditions  are  quite  different.  Thus  let  AI  and  B2  be 
transmitters,  while  BI  and  A2  receive  (Fig.  396). 

Everything  now  depends  upon  the  distance  of  AI  from  A2  and  of  BI 
from  BZ*  If  this  distance  is  only  a  small  part  of  the  wave-length,  it  will 
be  impossible  for  A2  to  get  the  telegrams  from  B2  without  hearing  the 
signals  from  its  neighbor  A  i  whose  waves  have  a  tremendous  amplitude 
at  so  short  a  distance  from  the  transmitter.  But  if  the  stations  AI  and 


Az,  as  well  as  BI  and  B2,  are  relatively  far  apart,  then  of  course  service 
between  the  two  pairs,  AiBi  and  B2A2,  can  be  maintained  without 
mutual  interference.  Just  how  far  apart  the  neighboring  stations  must 
be  depends  upon  the  ranges  of  the  stations,  the  difference  between  their 
wave-lengths,  the  sharpness  of  tuning  of  the  receivers  [Art.  180]  and  also 
upon  whether  the  transmitters  are  single  or  double  wave  transmitters,  the 
former  being  decidedly  more  advantageous.* 

If,  even  to  the  present  day,  frequent  complaints  of  interference 
between  stations  are  still  heard,296  imperfect  design  of  the  transmitters 
(high  damping)  and  receivers  is  undoubtedly  largely  responsible  for  this. 
It  must  be  remembered  that  with  the  great  number  of  shore  and  ship 
stations  now  in  operation  it  would  have  been  impossible  to  maintain 
even  a  passable  service  using  the  old  methods,  whereas  with  modern 
systems  the  service  on  the  whole  presents  no  great  difficulties. 

d.  Stations  arranged  for  tone  transmission  and  operating  on  the 
acoustic  or  mechanical  resonance  principle  [Art.  185]  are  least  affected  by 
interference.  For  here  interference  need  really  be  feared  only  if  the 
disturbing  transmitter  has  the  same  tone  as  well  as  the  same  wave-length. 

185.  Methods  for  Preserving  Secrecy  of  Messages. — The  fact  that 
tuning  does  not  in  itself  suffice  to  guard  the  secrecy  of  messages  is  a  great 
disadvantage!  for  many  purposes  (as  in  army  and  navy  work). 

*  The  NAT.  ELEC.  SIG.  Co.  (FESSENDEN)  makes  the  following  guarantee:  Given 
three  stations  AI,  Az  and  B2  of  equal  range.  If  the  distance  Ai—Az  is  1  per  cent,  of 
the  distance  A2-B2,  and  the  wave-lengths  differ  by  3  per  cent.,  A2  will  not  be  disturbed 
by  AI.  In  fact  with  standard  sets  a  difference  of  %  Per  cent,  in  wave-lengths  is 
claimed  to  be  sufficient  to  prevent  interference.  Reports  of  tests  indicate  that  this 
company's  apparatus  really  gives  very  fine  results  in  this  respect.296" 

t  On  the  other  hand  this  is  a  direct  advantage  for  distress  calls  at  sea,  where  it  is 
important  that  as  many  ships  as  possible  hear  the  call  for  help. 


RECEIVERS  331 

The  interception  of  messages  by  stations  other  than  those  called,  can 
be  prevented  to  some  extent  by  telegraphing  so  rapidly  that  such 
relays  as  are  customarily  used  will  no't  respond  and  only  specially  trained 
operators  will  be  able  to  read  the  messages  in  the  telephone.*  Further- 
more the  apparatus  can  be  so  arranged  that  the  wave-length  is  easily 
and  rapidly  changed  and  then  vary  the  wave-length  in  accordance  with  a 
prearranged  program,  perhaps  automatically .  f  This  method  makes  it 
very  difficult  for  an  uncalled  listener  to  tune  his  receiver  to  the  rapid 
variations,  but  it  is  of  no  avail  against  untuned,  highly  sensitive  receivers. 
Probably  all  such  methods  as  those  described  must  be  regarded  as  more  or 
less  makeshifts,  to  be  used  only  when  absolutely  necessary  and  which 
are  successful  only  in  special  cases.  The  following,  however,  are  im- 
portant effective  methods  for  providing  secrecy. 

a.  A  galvanometer  whose  natural  oscillations  are  slightly  damped 
(about  like  the  WIEN  vibration  galvanometer)  or  a  telephone  having  a 
diaphragm  whose  natural  oscillations  are  slightly  damped  or,  again,  a 
telephone  combined  with  a  closed  spherical  resonator2970  is  used  in  the 
receiver.  These  respond  well  only  if  the  frequency  of  the  interruptions 
in  the  transmitter  is  the  same  as  their  own  natural  periodicity.  This  is 
mechanical  tuning. % 

The  "sound  intensifier"  of  the  TELEFUNKEN  Co.  with  its  oscillating 
armature  [Art.  1666]  also  belongs  to  this  class  of  apparatus. 

In  all  such  arrangements  assuming  that  the  oscillating  mechanical 
system  is  tuned  to  the  discharge  frequency  of  the  transmitter,  the  curve 
of  the  oscillations  is  like  that  shown  in  Fig.  135;  i.e.,  the  amplitude  of 
the  oscillations  rises  gradually,  first  reaching  its  maximum  after  several 
periods,  the  number  of  which  depends  upon  the  decrement  of  the  oscillat- 
ing system;  both  this  number  of  periods  and  the  maximum  amplitude 
increase  as  the  decrement  decreases. 

Herein  lies  the  explanation  of  why  in  all  cases  of  such  mechanical  tuning 
the  sensitiveness  of  the  arrangement  depends  upon  the  rapidity  of  operation 
(i.e.,  of  telegraphing).  For,  in  order  to  take  full  advantage  of  the  sensi- 
tiveness, every  signal  must  last  long  enough  for  the  oscillating  system  to 
attain  its  maximum  amplitude.  If  the  telegraphing  is  done  so  rapidly 
that  the  duration  of  the  individual  signals  is  not  sufficient  to  reach  the 
maximum  amplitude,  the  sensitiveness  will  be  correspondingly  reduced. 

The  decrement  remaining  constant,  the  time  required  by  the  oscillat- 
ing system  to  reach  its  maximum  amplitude  increases  as  the  period 
lengthens,  i.e.,  as  the  discharge  frequency  is  reduced.  For  this  reason, 
such  devices  for  mechanical  tuning  were  of  little  practical  use  as  long  as  it 

*  This  method  was  tried  at  one  time  by  the  MARCONI  Co.  and  by  the 
DE  FOREST  Co. 

t  This  method  was  adapted  by  the  TELEFUNKEN  Co.  at  one  time. 

J  The  first  proposal  of  such  a  method  was  probably  made  by  A.  BLONDEL. 


332  WIRELESS  TELEGRAPHY 

was  customary  to  work  with  low  frequencies,  as  this  greatly  limited  the 
permissible  rapidity  of  operation.  The  adoption  of  high  discharge 
frequencies  in  the  transmitter  has  made  the  use  of  mechanical  resonance 
in  the  receiver  possible  without  any  great  detriment  to  rapidity  of 
signaling.  Nevertheless,  even  to-day  the  use  of  mechanically  resonant 
receivers  in  conjunction  with  automatic  transmitters  operating  at  very 
high  speeds  offers  great  difficulties. 

b.  Another  method  has  been  proposed  repeatedly  from  the  earliest 
days  of  wireless  telegraphy.  It  is  based  upon  transmitting  each  signal, 
say  each  MORSE  dot,  not  as  a  single  discharge,  but  as  a  series  of  periodic 
discharges  occurring  at  certain  fixed  equal  intervals.  The  receiver  is 
then  so  adjusted  that  it  will  respond  only  to  oscillations  occurring  at  these 
definite  intervals. 

Probably  the  only  apparatus  of  this  kind  which  were  used  in  practice 
were  those  of  ANDRES  BuLL298  and  of  HovLAND.298  They  were  rather 
complicated  and  will  not  be  described  in  detail  here.  But  it  should  be 
pointed  out  that  in  practical  tests  these  apparatus  gave  good  results. 
There  can  hardly  be  any  question  that  these  apparatus,  when  properly 
designed  and  constructed  for  reliability  in  operation,  provide  an  almost 
perfect  protection  not  only  against  the  "picking  up"  of  messages  by  stations 
not  called  or  intended  to  receive  them,  but  also  against  atmospheric  dis- 
turbances; on  the  other  hand  it  is  just  as  true  that  their  complication 
limits  these  apparatus  to  certain  special  work. 

3.  RECEIVERS  FOR  UNDAMPED  OSCILLATIONS 

186.  General. — For  recording  reception,  for  which  thermal  and 
crystal  detectors  and  the  EINTHOVEN  string  galvanometer  (photographic 
method)  are  generally  used,  conditions  are  much  the  same  for  undamped 
as  for  damped  oscillations.  The  secondary  circuit  of  the  receiver  is  made 
as  slightly  damped  as  possible,  is  loosely  coupled  to  the  antenna  [see  Art.  175] 
and  may  react  in  any  way  upon  the  detector. 

But  for  telephone  reception  a  decided  difference  is  encountered  between 
damped  and  undamped  oscillations;  the  arrangements  for  receiving 
damped  oscillations,  described  in  Art.  165,  can  not  be  used  without 
modification  for  undamped  oscillations.  For  in  telegraphing  a  dash  of 
the  MORSE  code,  the  excitation  of  the  wave  indicator  would  displace  the 
telephone  diaphragm  from  its  normal  position  at  the  beginning  of  the 
dash,  causing  a  click  to  be  heard  and  nothing  more,  as  the  telephone 
diaphragm  remains  displaced  in  a  fixed  position  just  as  long  as  the  waves 
from  the  transmitter  keep  coming  in  and  the  wave  indicator  remains 
excited.  Hence  dashes  and  dots  could  not  be  distinguished  as  both  would 
be  heard  simply  as  clicks. 

This  difficulty  can  be  overcome  by  sending  the  oscillations  out  in  a 


RECEIVERS  333 

series  of  "wave  trains"  obtained  by  means  of  a  kind  of  interrupter 
in  the  transmitter.  It  is  much  simpler,  however,  to  provide  the 
interrupter  at  the  receiving  end,  using  it  to  alternately  make  and  break 
the  connection  of  the  wave  indicator  to  the  oscillating  circuit.  Then 
the  telephone  diaphragm  is  displaced  at  each  "make"  and  returns 
to  its  normal  zero  position  at  each  "break."  That  is,  the  motion  of  the 
diaphragm  has  the  same  frequency  as  the  interrupter.  Consequently  as 
long  as  waves  strike  the  receiver,  the  tone  of  the  interrupter  is  heard  in 
the  telephone,  being  audible  for  relatively  long  and  short  periods  as  MORSE 
dashes  and  dots  are  transmitted. 

In  telegraphing  with  damped  oscillations,  an  interrupter  would  like- 
wise be  needed  if  the  discharge  frequency  were  above  that  (several  thou- 
sand per  second)  of  easily  audible  sounds.  This  condition  is  easily  ob- 
tained with  quenched  spark  gaps  and  D.C.  operation,  but  to  the  Author's 
knowledge,  has  never  been  used  in  radio-telegraph  practice,  being  re- 
stricted to  radio-telephony. 

187.  Methods  Employing  the  Ordinary  Detector. — a.  Fig.  397  illus- 
trates diagrammatically  one  of  the  arrangements  used  for  the  reception  of 
undamped  oscillations  (V.  POULSEN,  C. 
LoRENZ299).  The  condenser  circuit  drawn 
in  heavy  lines  is  the  secondary  of  the  ^" 

receiver;  it  is  as  slightly  damped  as  possi- 
ble and  very  loosely  coupled  to  the 
antenna.  The  interrupter,  U,  which  I  I  I  C7 

operates  on  the  principle  of  the  electric 
bell  or  buzzer,  alternately  connects  and     JL 
disconnects  the  detector  and  its  auxili-  -p^   007 

i1  JG.  oy  < . 
aries  to  and  from  the  secondary  circuit 

several  hundred  times  per  second.  This  arrangement  can  of  course  be 
varied  in  a  great  number  of  ways. 

6.  The  interrupter  used  in  this  method  is  something  more  than  a 
necessary  evil.  It  has  a  certain  decided  advantage. 

It  has  been  shown  that  it  is  of  the  greatest  importance,  both  for  the 
sharpness  of  tuning  [Art.  180c]  as  well  as  for  range  [Art.  676]  to  have  as 
little  damping  as  possible  in  the  secondary. 

As  long  as  the  detector  is  connected  to  the  secondary,  the  energy  (as 
long  as  it  remains  in  the  vicinity  of  the  critical  value  [Art.  1626]  of  the 
detector)  which  is  not  converted  or  only  partly  converted  into  direct- 
current  energy,  is  consumed  in  the  detector.  In  the  auxiliary  apparatus 
and  their  connecting  leads  energy  losses  can  hardly  be  entirely  eliminated, 
in  spite  of  the  insertion  of  choke  coils. 

But  when  using  an  interrupter,  no  such  loss  can  occur  in  the  wave 
indicator  or  in  the  auxiliary  apparatus  whenever  these  are  disconnected. 
The  amplitude  of  the  oscillations  in  the  secondary  circuit  and  hence  the 


To 

Telephone 


334  WIRELESS  TELEGRAPHY 

energy  stored  in  it,  rise  to  a  very  high  value.  Then  when  the  interrupter 
connects  the  wave  indicator  into  the  circuit,  it  is  acted  upon  by  an  oscilla- 
tion of  very  great  amplitude  and  almost  all  the  energy  accumulated  in  the 
secondary  circuit  is  used  for  exciting  the  wave  indicator. 

POULSEN  seems  to  have  succeeded  in  reducing  the  decrement  of  the 
secondary  circuit  to  0.003  in  this  way.300  This  could  not  be  attained  if  a 
wave  indicator  with  its  accessories  were  continuously  in  circuit. 

&  A  further  advantage  of  the  interrupter  is  the  possibility  of  pro- 
ducing a  musical  tone  in  the  telephone  by  suitable  connections  and  so 
obtain  to  some  extent  the  same  advantages  secured  by  means  of  a  tone 
transmitter  with  damped  oscillations. 

188.  The  Ticker.301 — a.  The  so-called  "ticker"  method  devised  by 
POULSEN,  in  which  none  of  the  wave  indicators  described  in  Chap.  X 
is  used,  is  shown  in  Fig.  398.  Here  U  is  the  interrupter  and  the  secondary 

circuit  proper  is  drawn  in  heavy  black  lines. 
Cf  is  a  very  large  condenser  of  several 
tenths  of  a  microfarad  capacity,  while  C 
has  only  a  few  thousandths  of  a  microfarad 
T  capacity.  Many  modifications  of  this  ar- 
rangement have  been  devised.* 

b.  The  basic  idea  in  POULSEN'S  arrange- 
ments (Fig.  398)  is  as  follows :     As  long  as 
-p          _  condenser    Cf    is    disconnected    from    the 

oscillating  circuit  CSz,  the  latter  accumu- 
lates a  relatively  large  amount  of  energy.  Then,  when  the  ticker 
connects  the  large  condenser  C'  in  parallel  to  the  small  condenser,  C,  Cr 
takes  the  major  part  of  the  current  and  of  the  stored  energy,  so  that 
it  obtains  a  relatively  high  charge,  which  upon  discharging  through  the 
telephone,  T,  causes  a  click  to  be  heard  in  the  latter.  Even  though  the 
procedure  may  be  somewhat  more  complicated  in  its  details  than  here 
outlined,  the  essential  features  of  what  occurs  are  as  just  described. 

c.  The  sensitiveness  of  this  arrangement  for  telephone  reception 
seems  to  be  greater  than  for  methods  using  any  of  the  best  wave  detectors 
described  in  Chap.  X.  The  latter  all  have  a  low  efficiency,  i.e.,  the 
direct-current  energy  delivered  by  them  is  only  a  small  fraction  of  the 
high  frequency  energy  supplied  to  them  [Art.  1626].  Too  great  a  loss  is 
involved  in  the  double  transformation,  first  from  electrical  energy  to 

*  The  following  arrangement  (TELEFTJNKEN  Co.302)  is  very  interesting.  The 
interrupter  U  in  Fig.  398  is  replaced  by  a  rectifying  detector  allowing  current  to  flow 
in  one  direction  only.  The  interrupter  is  inserted  between  C'  and  the  telephone  T. 
The  unidirectional  current  flowing  through  the  detector  charges  condenser  C',  which 
can  not  discharge  through  S2  on  account  of  the  detector.  As  the  interrupter  alter- 
nately connects  and  disconnects  the  telephone  T  to  and  from  condenser  C",  the 
latter  discharges  through  the  telephone  when  they  are  connected  and  is  recharged 
when  T  is  disconnected. 


RECEIVERS 


335 


heat  and  then  back  from  heat  to  electrical  energy.  In  the  ticker,  on  the 
other  hand,  there  is  practically  no  real  energy  transformation,  for  the 
charge  momentarily  stored  in  condenser  C"  (Fig.  398)  is  directly  dis- 
charged through  the  telephone.  Occasional  irregularities  in  the  inter- 
rupter, causing  the  "make"  and  "break"  to  occur  at  the  wrong  instant, 
will  have  but  little  effect  in  reducing  the  efficiency  if  the  condenser  circuit 
CS2  (Fig.  398)  is  only  slightly  damped. 

With  good  construction  of  the  interrupter,  its  operation  is  said  to-be 
very  regular  and  reliable.  On  the  other  hand,  it  does  not  seem  possible 
to  obtain  a  pure  tone  in  the  telephone  and  so  secure  the  same  freedom 
from  atmospheric  disturbances  with  the  ticker  as  is  obtainable  with  the 
tone  transmitter  [Art.  1836].  This  constitutes  a  serious  disadvantage, 
particularly  in  the  tropics. 

189.  Construction  of  Interrupter  for  Ticker  Method.  —  The  construc- 
tion of  a  good  practical  interrupter  for  use  in  the  ticker  systems,  is  not  so 
simple  as  might  at  first  sight  appear. 

a.  The  arrangement,  which  is  probably  in  widest  use  at  present,  is 
shown  diagrammatically  in  Fig.  399  :  b  is  an  electromagnet  facing  the 
small  armature  c,  which  is  vibrated,  just  as  in  an 
electric  bell  or  buzzer,  by  a  battery  connected  to  the 
winding  of  the  magnet.  The  spring  d,  on  which  the 
armature  is  mounted,  is  fastened  to  a  plate  having  a 
slight  spring  to  it.  Resting  on  this  plate  is  a  small 
piece  of  metal,  c,  to  which  a  fine  gold  wire,  /,  is  at- 
tached. This  gold  wire  together  with  the  small 
adjustable  wire  brush,  g,  constitutes  the  ticker  con- 
tact. 

The  sensitiveness  of  this  arrangement  can  be  in- 
creased by  using  a  telephone  diaphragm  of  low  damp- 


FIG. 399. 


ing  to  whose  natural  oscillation  the  ticker  is  tuned  [see  Art.  185a]. 

b.  L.  W.  AusTiN303  has  described  a  rotary  interrupter  which  is  said  to 
be  particularly  well  suited  for  use  in  conjunction  with  the  ticker.  It 
consists  of  a  highly  polished  copper  or  nickel  disc  which  is  kept  in 
rotation,  while  a  fine  copper  wire  brushes  against  the  disc  under  very 
light  pressure. 

190.  Special  Arrangements  for  Undamped  Oscillations.  —  a.  The 
heterodyne,  receiver  of  R.  A.  FESSENDEN.304  The  principle  of  this 
receiver  is  well  illustrated  by  the  following  description  of  one  form  in 
which  it  has  been  constructed.  The  telephone,  instead  of  having  the 
usual  permanent  magnet,  has  a  core  of  fine  iron  wires  within  a  winding 
and  instead  of  an  iron  diaphragm,  has  one  of  mica  carrying  a  coil  of  fine 
wire. 

The  oscillations  induced  in  the  receiver  by  the  incoming  waves  are 
led  through  the  coil  in  the  diaphragm.  A  high  frequency  current,  whose 


336  WIRELESS  TELEGRAPHY 

frequency,  Nf,  differs  somewhat  from  that,  N,  of  the  incoming  oscillations 
is  sent  through  the  winding  of  the  electromagnet. 

The  force*  exerted  upon  the  diaphragm  coil  by  the  field  of  the  iron 
wire  core  varies  periodically.  Consequently,  the  telephone  diaphragm 
oscillates  at  a  frequency  which  =  N  —  Nf,  as  will  be  evident  from  a 
simple  consideration  of  the  facts.  Hence,  if  N  and  Nr  are  so  chosen  that 
the  frequency  equal  to  their  difference  lies  within  the  range  of  audible 
tones,  this  tone,  N  —  N',  will  be  heard  in  the  telephone. 

b.  R.  GoLDSCHMiDT's305  method.  The  principle  upon  which  this 
method  is  based  is  easily  understood  from  a  consideration  of  Art.  122. 
The  oscillations,  of  frequency  N,  which  are  induced  in  the  receiver  by  the 
waves  from  the  transmitter,  are  led  through  a  fixed  coil  (S  in  Fig.  261). 
In  the  revolving  field  of  this  coil  there  is  a  movable  coil,  R,  which  rotates 
at  N'  revolutions  per  second.  Then  there  will  be  induced  in  this  movable 
coil  a  current  of  frequency  N  —  Nf,  which  under  proper  conditions  can 
be  heard  in  a  telephone,  even  though  N  and  N'  individually  lie  far  outside 
the  range  of  audible  tones. 

In  practice,  of  course,  the  fixed  and  movable  coils,  S  and  R,  are  re- 
placed by  the  stator  and  rotor  respectively  of  a  high  frequency  generator. 
By  adjusting  the  speed  of  the  machine,  the  rotor  currents  are  made 
audible  in  a  connected  telephone. 

191.  Practical  Achievements. — a.  The  question,  to  what  extent 
tuning  the  receiver  can  prevent  disturbance  from  other  stations  and 
secure  privacy  of  messages  when  working  with  damped  oscillations  was 
discussed  in  Art.  184.  The  question  now  arises  whether  the  use  of 
undamped  oscillations  will  materially  alter  these  conditions. 

In  regard  to  securing  secrecy  of  messages  it  is  evident  from  Art.  184a 
alone,  that  undamped  oscillations  have  a  great  advantage  over  damped 
oscillations;  for  the  lower  the  amplitude  required  to  attain  a  given  range, 
the  more  difficult  it  becomes  to  "pick  up"  a  telegram. 

For  this  same  reason  it  would  seem  that  undamped  oscillations 
should  also  provide  a  greater  protection  against  intentional  disturbance 
by  other  stations.  Actually,  however,  this  advantage  is  not  very  great 
when  compared  with  well-designed  stations  operating  with  damped 
oscillations. 

b.  In  regard  to  interference  between  two  stations  (and  the  same 
applies  to  the  use  of  undamped  oscillations  in  multiplex  telegraphing),  we 
would  expect  that  undamped  oscillations,  in  view  of  the  very  loose 
coupling  in  the  receiver  and  the  very  low  damping  of  the  secondary  cir- 
cuit, would  offer  very  decided  advantages  and  secure  particularly  sharp 
tuning.  And  this  would  undoubtedly  be  the  case  if  the  same  conditions 

*  Or  rather,  to  be  more  exact,  its  mean  value  during  one  period.  Of  course,  this 
force  varies  continuously  during  each  period,  but  these  rapid  variations  do  not  come 
into  consideration  for  the  motion  of  the  diaphragm. 


RECEIVERS  337 

obtained  in  the  transmitter  as  with  damped  oscillations.  But  in  practice 
the  frequency  of  the  undamped  oscillations  is  never  quite  constant, 
whether  they  are  produced  by  a  high  frequency  alternator  or  by  an  arc 
generator.  As  to  just  how  much  the  frequency  has  been  found  to 
fluctuate  in  the  high  frequency  alternators  which  have  been  built  to  date, 
nothing  has  been  published  so  far  as  the  author  knows.  With  the  arc 
method,  it  seems  that  a  sharpness  of  tuning  fully  as  good  as,  but  not  better 
than  the  best  obtainable  with  damped  oscillations  can  be  secured;*  and 
there  is  no  need  for  any  still  greater  sharpness. 

*  P.  O.  PEDERSEN186  states  that  in  the  method  of  transmitting  used  by  him  [Art. 
127 c]  a  dissonance  of  ^  per  cent,  in  the  transmitted  wave  sufficed  to  prevent  recep- 
tion. This  would  indicate  a  very  great  sharpness  of  tuning. 


22 


CHAPTER  XIII 
DIRECTIVE  TELEGRAPHY 

192.  Characteristic  of  the  Distance  Effect. — The  object  in  view  in 
"directive  telegraphy"  is  to  so  confine  the  radiation  of  waves  from  the 
transmitter  to  a  narrow  or  rather  an  acute  angle,  that  only  receivers 
located  within  this  angle  will  be  in  the  path  of  the  waves.  Actual  ac- 
complishment, so  far;  consists  in  transmitters  whose  waves  radiating  in 
different  directions  have  widely  differing  amplitudes. 

a.  The  following  method  is  convenient  for  obtaining  a  picture  or 
"curve"  of  the  power  of  any  given  transmitter  to  direct  its  waves.  The 
amplitude  of  the  waves  is  measured  from  point  to  point  on  a  circle  (of 
suitable  radius)  whose  center  is  at  the  transmitter  and  the  values  so 


FIG.  400. 

obtained  are  plotted  as  vectors  in  the  directions  or  angles  corresponding 
to  each  amplitude  (Fig.  400).  The  curve  obtained  by  joining  the  ends 
of  the  vectors  is  the  "characteristic  of  the  distance  effect"  and  gives  a 
simple  picture  of  the  usefulness  of  the  particular  transmitter  for  directive 
signaling. 

It  is  self-evident  that  the  characteristic  of  all  symmetrical,  vertical 
transmitters  is  a  circle.  If  the  characteristic  is  of  the  form  shown  in  Fig. 
401,  the  obvious  conclusion  is  that  the  transmitter  in  question  emanates 
waves  in  all  directions,  but  its  effect  in  the  direction  SB  is  considerably 
less  than  in  all  other  directions.  The  case  illustrated  in  Fig.  402  is  much 
more  desirable  for  directive  transmission;  no  waves  are  sent  out  in  the 
direction  SB,  practically  all  being  concentrated  in  the  direction  SA,  so 
that  in  directions  diverging  even  only  very  slightly  from  SA,  the  effect 
is  very  much  less.  A  transmitter  having  this  characteristic  would  be  a 
practical  solution  of  the  problem  of  directive  telegraphy;  its  effect  would 
be  confined  to  an  extremely  acute  angle. 

6.  For  detectors  which  react  upon  the  current  effect,  reception  de- 
pends, not  upon  the  amplitude  of  the  waves,  but  upon  the  square  of  the 

338 


DIRECTIVE  TELEGRAPHY 


339 


amplitude.  Hence,  to  obtain  a  picture  of  the  distance  effect  of  a  trans- 
mitter with  respect  to  a  receiver  of  this  type  the  squares  of  the  wave 
amplitudes  in  the  different  directions  must  be  plotted  as  vectors  in  the 
diagram.  The  characteristic  of  amplitude  squares  is  distinguished  from 
that  of  the  amplitudes  in  that  it  is  much  less  like  a  circle  in  form*  and, 
therefore,  is  much  better  suited  to  the  purpose  in  view.  It  follows  that 
detectors  which  react  upon  the  current  effect,  as,  e.g.,  thermal  detectors, 


FIG.  402. 


FIG.  401. 

are  much  better  adapted  for  directive  signaling  than  those  whose  action 
depends  upon  the  amplitude  (first  power)  of  the  oscillations  [see  Art. 
163a]. 

In  what  follows,  the  simple  characteristics  (first  powers  of  the  ampli- 
tudes) are  plotted  throughout,  as  these  (but  not  the  squares  of  the 
amplitudes)  also  serve  as  a  direct  measure  of  the  range  of  the  transmitter 
in  the  various  directions  (see  c). 

c.  The  characteristic  of  a  transmitter  generally  depends  upon  the 
distancef  at  which  the  amplitudes  are  measured.  Strictly  speaking, 
therefore,  we  can  only  refer  to  the  characteristic  of  a  transmitter  at  a 
given  distance.  • 

However,  as  the  distance  becomes  very  great  in  comparison  with  the 
wave-length  employed,  then,  in  general,  further  increases  in  the  distance 
will  have  little  or  no  effect  upon  the  shape  of  the  characteristic.  Hence, 
we  are  justified  in  speaking  of  "the"  long  distance  characteristic  of  a 
transmitter.  This  same  characteristic  can  also  be  obtained  by  plotting 
the  ranges  of  the  transmitter  (for  a  given  receiver)  over  a  highly  con- 
ductive ground  J  as  vectors  in  the  various  directions. 

But  for  distances  which  are  not  large  compared  to  the  wave-length,  or 

*  Thus,  if  the  ratio  of  the  lengths  of  two  vectors  in  the  amplitude  characteristic  is 
1 : 2,  then  it  will  be  1 : 4  for  the  corresponding  vectors  in  the  characteristic  of  the  squares. 

t  In  this  and  what  follows  the  effect  of  the  distribution  of  land  and  water  and  other 
local  influences  upon  the  characteristic  is  not  taken  into  account;  the  ground  is  as- 
sumed to  be  homogeneous  in  all  directions. 

t  Otherwise  absorption  would  complicate  the  conditions. 


340  WIRELESS  TELEGRAPHY 

perhaps  even  shorter,  the  shape  of  the  characteristic  is  largely  dependent 
upon  the  distance.  Consequently  a  characteristic  determined  by 
measurements  relatively  close  to  the  transmitter  gives  no  definite  indica- 
tion of  the  long  distance  characteristic  and  can  not  serve  as  a  measure  of 
the  practical  usefulness  of  the  transmitter.  A  transmitter  whose  character- 
istic at  a  short  distance  appears  very  advantageous  for  directive  signal- 
ing, may  nevertheless  have  a  long  distance  characteristic  which  is  almost 
a  circle. 

1.  THE  FIRST  ATTEMPTS 

193.  Use  of  Reflectors. — To  attain  the  almost  ideal  case  represented 
by  Fig.   402,   an  adaptation  of  HERTZ'S  parabolic  mirror  method  as 
employed  in  his  well-known  experiments,  readily  suggests  itself.     In  fact 
it  has  often  been  proposed  to  use  such  reflectors  of  sheet  metal  or  wires 
to  send  the  waves  out  in  a  single  direction.     MARCONI  also  conducted 
some  early  experiments  with  reflectors. 

This  was  reasonable  enough  as  long  as  it  was  customary  to  work  with 
very  short  waves.  In  modern  practice,  however,  the  wave-lengths  em- 
ployed range  from  300  to  6000  m.  or  more.  A  reflector,  to  have  the 
desired  result,  as  obtained  in  optics  or  in  HERTZ'S  experiments,  would 
have  to  have  dimensions  commensurate  with  the  wave-length.  This 
requirement  is  sufficient  to  eliminate  the  practical  use  of  reflectors  for  the 
wave-lengths  in  question. 

194.  Attempts  at  Screening,  J.  ZENNECK. — A  characteristic  of  the 
kind  shown  in  Fig.  401,  i.e.,  with  very  little  radiation  in  one  direction 
(SB  in  Fig.  401),  was  obtained  by  the  author  as  early  as  1900  in  the 
following  manner. 

At  a  station,  A  (Kugelbake,  near  Cuxhaven),  two  vertical  wires, 
did2  (Fig.  403),  about  30  m.  long  were  suspended  about  6  m.  apart. 


A 

X*  X 

/ 


FIG.  403. 

The  receiving  station,  B  (Altenbruch  Lighthouse)  was  situated  about 
9  km.  from  A  and  nearly,  though  not  quite,  in  line  with  did^.  With 
only  one  aerial  wire  in  use  the  messages  sent  out  could  be  well  under- 
stood at  the  receiving  station,  but  at  twice  this  distance  reception  was 
no  longer  possible,  so  that  we  were  working  with  a  safety  factor  of  a  bit 
less  than  2.  The  following  tests  were  then  made: 

1.  di  used  as  transmitting  aerial,  d2  not  grounded;  the  signals  were 
clearly  audible  at  B; 

2.  di  again  transmitting,  d2  grounded;  no  reception  at  B; 


DIRECTIVE  TELEGRAPHY  341 

3.  c?2  transmitting,  di  grounded;  signals  clearly  received  at  B. 

From  1  and  2  it  was  concluded  that  it  is  possible  to  greatly  reduce  the 
range  in  a  given  direction  by  means  of  a  grounded  wire  parallel  to  the 
transmitting  aerial;  from  3,  that  this  does  not  materially  affect  the  range 
in  the  opposite  direction. 

The  results  of  the  experiment  left  no  doubt  that,  e.g.,  a  station  A 
(Fig.  404)  can  send  telegrams  to  another  station  B,  while  a  third  station 


FIG.  404. 

C,  at  the  same  distance  as  B,  does  not  receive  these  messages,  if  wire  d\ 
at  A  is  used  as  the  transmitter,  d3  is  grounded  and  d2  is  insulated  from  the 
ground.  Insulating  d3  and  grounding  d2  reverses  the  conditions  so  that 
C,  and  not  B,  receives. 

These  tests  were  taken  up  by  the  TELEFUNKEN  Co.  at  a  later  date  and 
the  results  verified.  It  was  here  shown  that  an  essential  factor  consists 
in  having  the  screening  aerial  tuned  to  the  transmitter  frequency,  which 
condition  was  really  fulfilled  in  the  tests  when  the  screening  aerial  was 
grounded.  These  tests  were  not  carried  out  far  enough  to  form  definite 
conclusions  of  just  what  can  be  accomplished  in  this  direction.* 

2.  METHODS  EMPLOYING  SEVERAL  ANTENNAE 

195.  The  Field  of  Several   Antennae. — General   Consideration. — If 

two  vertical  antennae,  oscillating  at  the  same  wave-length,  are  a  given 
distance  apart,  then  the  amplitude  of  the  resultant  wave  produced  by  the 
two  antennae  is  never  uniform  in  all  directions,  whether  or  not  the 
currents  in  the  two  antennae  are  in  phase.  At  any  distant  point  P 
(Fig.  405),  the  two  waves  which  are  there  superimposed  have  traveled 
different  distances  and  in  view  of  this  difference  (AD,  Fig.  405)  they  are 
not  in  phase  with  each  other  [Art.  206].  This  phase  difference  <p — as- 
suming the  currents  in  the  two  antennee  to  be  in  phase — is  proportional 

*  The  explanation  of  the  action  of  this  arrangement  lies  partly  at  least  in  the  fact 
that  the  transmitter  induces  oscillations  in  the  screening  aerial  whose  phase  is  dis- 
placed from  that  of  the  transmitter  oscillations. 


342 


WIRELESS  TELEGRAPHY 


to  the  ratio  of  the  difference  in  the  distance  traveled  to  the  wave-length, 
as  given  by 

AD    2ird 

<p  =  2ir  -r—  =  -r—  cos  & 
X         X 

where  the  angle  &  is  a  measure  of  the  direction  in  which  the  point  P  lies 
and  d  is  the  distance  between  the  two  antennae. 

But  this  phase  difference,  <p,  and  hence  also  the  angle  $,  affect  the 
amplitude  of  the  resultant  field  at  P,  which  is  obtained  from  the  in- 
dividual amplitudes  by  means  of  the  familiar  vector  diagram.  Thus  in 
Fig.  406,  the  length  of  vector  OB  is  proportional  to  the  amplitude  of  the 
field  at  P  due  to  antenna  B,  while  vector  OA  represents  the  field  due  to 
antenna  A;  angle  BOA  is  equal  to  the  difference  in  phase  between  the 
two  fields,*  i.e.,  in  this  case,  it  is  equal  to  the  phase  difference,  ^,  of  the 


FIG.  405. 


FIG.  406. 


two  currents  in  the  antennae  A  and  B,  plus  the  phase  difference  in  the 
waves  <p  caused  by  their  difference  in  travel.  The  diagonal  OC  of  the 
parallelogram  OABC  represents  the  amplitude  and  phase  of  the  resultant 
field  at  P. 

From  this  construction  it  is  evident  that  the  length  of  OC  and,  hence, 
the  amplitude  of  the  resultant  field  at  point  P  depend  upon  the  angle  <p 
and  therefore  upon  the  direction  of  P  with  respect  to  AB.\ 

196.  The  Field  of  Several  Antennae. — Special  Cases.306— The  follow- 
ing special  cases,  involving  two  antennae  alike  in  all  respects,  are  of  par- 
ticular interest: 

1.  The  currents  in  the  two  antennae  are  equal  in  phase  (^  =  0°)  and 
amplitude. 

2.  The  currents  are  of  opposite  phase  (^  =  180°),  the  amplitudes 
equal. 

*  The  feathered  arrow  in  Fig.  406  indicates  the  direction  of  "lead,"  i.e.,  the  current 
in  antenna  A  "lags"  behind  that  in  B  by  the  angle  ^. 

t  If  the  amplitudes  of  the  fields  of  both  antenna  are  equal  to  each  other  and  are 
Eo,  then  the  amplitude  Ero  of  the  resultant  field  is  given  by 

<p  +  ^  Vird 

Ero  —  2Eo  cos  — ^—    =  2E o  cos    —  cos  $  + 
Z  \_\ 

which  also  determines  the  characteristic  of  the  distance  effect.307 


DIRECTIVE  TELEGRAPHY 


343 


3.  The  currents  have  equal  amplitudes  as  before,  but  their  phase 
displacement,  ^,  is  so  great,  that  their  resultant  effect  is  neutralized 
either  in  direction  OA  or  direction  OB  (Fig.  405)  in  the  plane  of  the 

antennae.     For  this  purpose  the  value  of  ^  must  be  either  TT ^-  or 

r  +'  —  (Fig.  405). 

a.  If  the  currents  in  the  two  antennae  are  equal  in  both  amplitude  and 
phase  (3?  =  0),  then  it  follows  directly  from  Art.  25c  that  in  a  direction 
perpendicular  to  the  plane  of  the  antennae  (#  =  90°  or  270°)  the  resultant 
amplitude  is  simply  the  sum  of  the  individual  amplitudes  of  the  two 
fields,  i.e.,  the  amplitude  of  the  resultant  field  Ero  =  2E0,  if  EQ  is  the 
amplitude  of  the  field  of  each  antenna.  In  the  plane  of  the  antennae,  the 
resultant  amplitude  is  not  the  algebraic  sum,  as  a  phase  difference, 

<p  =  -r— ,  exists  here;   accordingly  the  resultant  amplitude  is  always 

A 

less  than  2E0,  becoming  smaller  as  the  phase  difference  <p  approaches 
180°  (?r)  or,  in  other  words,  as  the  distance  d  between   the   antennae 

approaches  ~.* 


FIG.  407. 


FIG.  408. 


In  Figs.  407  to  409  the  distance  effect  characteristics  of  such  a  pair  of 
antennae  are  drawn  for  various  values  of  d,  viz.,  d  =  -r  in  Fig.  407, 

d  =  ~  in  Fig.  408  and  d  =  X  in  Fig.  409.     Obviously  this  arrangement 

is  suitable  for  directive  signaling  only  when  the  distance  between  the 
antennae  is  about  one-half  the  wave-length. 

b.  If  the  currents  in  the  two  antennce  are  equal  in  amplitude,  but  have  a 
phase  difference,  ^f  of  180°,  the  two  fields  neutralize  each  other  in  the 
direction  perpendicular  to  the  plane  of  the  antennae.  Furthermore,  the 

*  In  that  case  the  amplitude  of  the  resultant  field  and  the  characteristic  of  the 
distance  effect  are  given  by 

Ero  =  2E0  cos  ~  = 


cos  I  — 


344  WIRELESS  TELEGRAPHY 

distance  effect  characteristic*  depends  largely  upon  the  distance  between 
the  antennae,  d,  as  compared  to  the  wave-length.  If  the  ratio  r-  is  very 

A 

small,  the  characteristic  practically  consists  of  two  circlesf  (Fig.  410). 

Even  if  d  =  ~,  the  characteristic  is  not  much  different  from  this  form 

z 

(Fig.  411).  But  if  the  distance  between  the  antennae  is  further  increased, 
the  characteristic  becomes  less  favorable  for  directive  telegraphy;  thus 
Fig.  412  represents  the  results  obtained  if  d  = 


FIG.  410.  FIG.  411. 


It  should  be  noted  that  with  the  antennae  very  dose  together  (    very 


small)  the  characteristic  has  a  relatively  advantageous  form.  One  thing 
however  must  not  be  forgotten.  The  amplitude  of  the  electric  field  in  the 
plane  of  the  antennae,  which  in  fact  is  the  maximum  amplitude  in  this 

case  (and  for  values  of  d  up  to^K  is  2EQ  sin  -.-•{     Accordingly  it  and, 

therefore,  the  maximum  range  and  practical  value  of  the  arrangement 
are  greatly  reduced  as  d  is  decreased. 

c.  In  the  third  special  case  under  consideration,  where  the  phase 
difference  >fr,  between  the  two  antenna  currents  is  so  chosen  that  their 
resultant  effect  is  zero  either  in  the  direction  OA  or  in  the  direction  OB 

(Fig.  405)  in  the  plane  of  the  antennae  (3f  =  TT  ±  -r—  j  ,  the  characteristics 

obtained  have  a  distinct  difference  from  those  obtained  in  the  other  two 
cases.  The  latter  always  consisted  of  two  symmetrical  halves,  so  that 

*  The  characteristic  is  determined  by  the  equation 


Ero  =  2E0  sin      =  2E0  sin   —  cos 


f  This  is  evident  from  the  fact  that  for  this  case  we  can  write :     Ero  =  2E0 .  ^ 

ird 
•rox.  =  2E0  .  -r~  cos  i 

A 

J  This  amplitude  is 


approx.  =  2E0 .  —  cos  tf  approx 

A 


2E0  X  1  for  d  =  %  X 
2E0  X  0.71  for  d  =  Y±  \ 
2EQ  X  0.31  for  d  =  Y^  \ 


DIRECTIVE  TELEGRAPHY  345 

the  same  range  is  obtained  in  any  two  directions  180°  apart;  the  arrange- 
ment is  said  to  be  "bilateral."  Transmitters  of  the  third  class  however  are 
"unilateral,"  i.e.,  the  ranges  in  any  two  directions  180°  apart  are  different. 
In  Figs.  413,  414  and  415  the  distance  effect  characteristics*  are  given 
for  the  following  cases:  d  <  >{2*  (Fig.  413);  d  =  Y±\  (Fig.  414);  d  = 
(dotted  curve,  Fig.  415);  d  =  %\  (full  line  curve,  Fig.  415). 


*** 

FIG.  413.  FIG.  414.  FIG.  415. 

Just  as  in  case  b  the  characteristic  becomes  unfavorable  for  directive 
signaling  in  this  case  also,  as  soon  as  the  distance  between  the  antenna  is 
made  more  than  one-fourth  of  the  wave-length,  whereas  very  small  distances 
between  the  antennae  are  very  advantageous.  But,  again  as  in  case  6,  the 

maximum  range  is  reduced  at  the  same  time  as  the  ratio  -  is  decreased. 

A 

197.  Double  Antennae,  One-half  Wave-length  Apart  (S.  G.  BROWN, 
A.  BLONDEL,  J.  STONE  STONE308). — a.  The  case  discussed  in  Art.  1966, 
which  is  particularly  advantageous  both  with  respect  to  directive  power 
and  range — two  similar  antennae  placed  a  half  wave-length  apart,  with 
their  currents  of  equal  amplitude  but  opposite  phase — has  been  fre- 
quently proposed  since  1899,  by  various  experimenters.  To  produce  the 
oscillations  the  antennae  are  joined  at  their  bases,  A  and  B,  by  a  conduct- 
ing circuit  which  is  suitably  coupled  [Art.  198a]  to  a  condenser  circuit. 
This  arrangement  is  not  entirely  identical  with  the  case  discussed  in 
Art.  1966,  for  to  the  effect  of  the  vertical  antennae  AC  and  BD  is  added 
that  of  the  horizontal  portion  AB,  which  under  certain  conditions 
[Arts.  2036  and  206]  may  be  quite  considerable. 

It  is  almost  self-evident  that  a  pair  of  antennae  of  the  kind  just  de- 
scribed will  serve  for  directive  reception,^  i.e.,  will  respond  with  varying 

*  If  the  phase  difference  is  so  chosen  that  the  fields  of  the  two  antennae  neutralize 
each  other  in  the  direction  OA  or  OB  (Fig.  405),  then  we  have 

Ero  =  2E0  sinT7^  (cos  &  -  1)1  or  E  ro=  2E0  sm\~  (cos  &  +  1)1 
LA  J  LA  J 

For  small  values  of  -  these  equations  may  be  simplified  into  Ero  =  2E0 .  —  (cos 

A  A 

*T1). 

f  For  this  purpose  a  detector  circuit  is  coupled  to  the  antenna  pair  at  the  anti-node 
of  current. 


346 


WIRELESS  TELEGRAPHY 


intensity  as  the  direction  of  the  approaching  waves  varies.  Thus  waves 
whose  direction  is  perpendicular  to  the  plane  of  the  antennae,  induce 
potentials  of  equal  phase  and  amplitude  in  both  antennae,  so  that  these 
would  neutralize  each  other  and  produce  a  zero  effect  in  the  system  shown 
in  Fig.  416.  But  waves  approaching  in  the  plane  of  the  antennae — if 
their  wave-length  is  2AB  (Fig.  416) — induce  potentials  of  opposite  phase 


FIG.  416. 

in  the  two  antennae,  so  that  their  effect  upon  the  oscillatory  system  is 
additive.* 

b.  A  somewhat  different  form  of  the  double  antenna  (Fig.  417)  has 
been  proposed  by  A.  BLONDEL.308  When  used  for  transmission,  the  same 
condenser  circuit  is  coupled  with  the  coils  S  and  S'  in  such  manner  that 
the  currents  in  the  two  antennae  will  be  of  opposite  direction.  Then,  so 


B  B1 


Cf 


FIG.  417. 

far  as  distance  effect  is  concerned,  the  currents  in  the  vertical  parts  AB 
and  A'B'  entirely  neutralize  each  other,  and  all  that  remains  is  the  effect 
of  the  currents  (of  opposite  direction)  in  parts  CD  and  C'D'  (whose  dis- 

*  The  distance  effect  characteristic,  at  least  for  the  vertical  portions  of  this  double 
receiving  antenna,  would  be  the  same  as  for  the  antenna  pair  when  used  for  transmit- 
ting, as  will  be  readily  understood  by  reversing  the  conditions  in  the  discussion  of 
Art.  196. 


DIRECTIVE  TELEGRAPHY 


347 


tance  apart  is  made  about  equal  to  a  half  wave-length)  and  of  the  cur- 
rents in  the  horizontal  portions  BC  and  B'C1 '. 

198.  The  Methods  of  E.Bellini  and  A.  Tosi.309 — a.  BELLINI  and  Tosi 
have  also  adapted  the  case  described  in  Art.  1966,  using  two  antennae 
with  currents  of  equal  amplitude  but  opposite  phase,  but  the  distance 
between  their  antennae  is  sometimes  only  slightly,  sometimes  much  less 
than  half  the  wave-length.  Instead  of  being  vertical,  however,  the 
antennae  are  slightly  inclined  (Fig.  418).  This  arrangement  has  the 
advantage  of  being  more  easily  suspended  from  a  single  mast.  When 
located  over  ground  of  very  high  conductivity  (sea  water)  the  action  of 


such  a  pair  of  inclined  antennae  is  not  much  different  from  that  of  a 
vertical  pair  of  the  same  height,  but  somewhat  closer  together  (as 
represented  by  the  dash-and-dotted  lines  in  Fig.  418).  But  over  ground 
of  relatively  low  conductivity,  the  distance  effect  characteristic  is  apt  to 
be  considerably  different  from  that  obtained  with  two  vertical  antennae 
[see  Art.  205].  In  this  last  case  the  horizontal  portion  AB  (Fig.  418)  is 
likely  to  have  a  material  effect. 

In  order  to  obtain  oscillations  of  opposite  phase  in  the  two  inclined 

antennae,  BELLINI  and  Tosi  make  use  of  the  second  upper  harmonic* — 

\ 

*  Corresponding  to  the  second  upper  harmonic  shown  in  Fig.  34.  The  fundamental 
oscillation,  in  which  A' ABB'  is  equivalent  to  one-half  the  wave-length,  can  also  be 
used  for  this  purpose. 


348 


WIRELESS  TELEGRAPHY 


third  harmonic — of  the  entire  system  [Art.  22]  (Fig.  418).  For  any  given 
distance  between  the  inclined  antennae,  the  upper  harmonic  is  obtained, 
say,  by  inserting  self-induction  (or  perhaps  condensers  also)  of  suitable 
dimensions.  The  oscillations  are  then  induced  by  means  of  a  condenser 
circuit,  CS,  Fig.  418,  tuned  to  the  frequency  of  the  desired  harmonic. 

When  this  arrangement  is  to  be  used  for  reception,  the  condenser  cir- 
cuit is  replaced  by  a  detector  circuit.  The  system  then  reacts  with  the 
greatest  intensity  upon  waves  whose  direction  lies  in  the  plane  of  the 
antennae. 

b.  With  the  arrangement  of  Fig.  418,  the  direction  of  maximum  wave 
amplitude  lies  in  the  plane  of  the  antennae.  If  this  direction  is  to  be 


FIG.  419. 

varied  at  will  it  is  necessary  to  turn  the  entire  system.  This  would  be 
impracticable  on  shipboard  and  particularly  on  fixed  land  stations.  In 
view  of  this,  BELLINI  and  Tosi  have  introduced  another  method  for 
obtaining  the  desired  result.*  They  combine  two  pairs  of  antennae  (AB 
and  AiBi,  Fig.  419),  each  being  of  the  form  illustrated  in  Fig.  418,  so  that 
their  planes  are  at  right  angles  to  each  other.  Similarly  the  coupling 
coils  /S'and  S"  (Fig.  419)  are  arranged  so  as  to  be  perpendicular  to  each 
other.  The  coil  S,  which  is  part  of  the  condenser  circuit  CS,  used  for 
excitation,  can  be  rotated  within  the  coils  Sf  and  S". 

If,  then,  the  distance  d  between  the  antennae  is  small  compared  to  the 

wave-length  (d  ^  gj  [Art.  1966]  a  very  simple  calculation309  will  bring  out 

the  following  facts: 

1.  The  direction  of  maximum  range  lies  in  the  same  plane  as  coil 
*A.  BLONDEL310  has  also  proposed  other  methods  for  securing  the  same  results. 


DIRECTIVE  TELEGRAPHY 


349 


S;*  the  amplitude  of  the  waves  in  this  direction  is  always  equal  to  the 
maximum  amplitude  of  a  single  pair  of  the  antennae,  independently  of 
the  position  of  S. 

2.  The  distance  effect  diagram  has  the  same  form,  that  of  Fig. 
410,  for  all  positions  of  S}  and  consists  of  two  tangent  circles,  whose  line 
of  centers  lies  in  the  plane  of  coil  S. 

But  if  the  distance  between  the  antennae  is  greater,  d  being  from 

-  to  ~,  then  condition  1  is  retained,  i.e.,  the  direction  of  maximum  range 
u  ^ 

lies  in  the  plane  of  S*  and  can  be  varied  at  will  by  rotating  S,  the 


0*270° 

FIG.  420. 

maximum  amplitude  does  not  remain  constant  for  all  positions  of  S; 
in  fact  it  has  its  greatest  value  for  /?  =  45°  and  /?  =  135°  and  its  minimum 
for  fi  =  0°  and  /3  =  90°  f  [see  Fig.  420,  which  gives  the  maximum  ampli- 
tudes for  all  the  different  positions  of  S,  i.e.,  different  values  of  0  (Fig. 
419)].  The  distance  effect  characteristic  is  also  changed  somewhat,  in 

*  When  these  antennae  are  mounted  on  shipboard,  the  metallic  masses  in  the  ship 
and  particularly  the  rigging  are  apt  to  affect  the  distribution,  so  that  the  direction  of 
the  maximum  wave  amplitude  no  longer  coincides  with  that  of  coil  S.  Then 
empirical  calibration  of  the  radio-goniometer  is  necessary  (see  what  follows). 

f  The  maximum  amplitudes  for  these  two  cases  differ  by  8  per  cent,  when  d  =  ^ 
and  by  24  per  cent,  when  d  =  ~ 


350 


WIRELESS  TELEGRAPHY 


this  case,  as  the  position  of  S  is  varied.     This,  however,  is  not  of  great 
practical  importance.* 

BELLINI  and  Tosi  have  combined  the  two  coupling  coils,  S'  and  S" 
together  with  the  movable  coil  S,  in  a  single  apparatus  called  the  trans- 
mitting "radio-goniometer"  (Fig.  421).  The  two  coils  S'  and  S" 
(Fig.  419)  are  wound  on  a  cylinder  inside  of  which  S  rotates. 


FIG.  421. 

For  the  reception  of  waves  tuned  to  the  goniometer,  the  so-called 
"receiving  radio-goniometer"  is  used,  which  is  the  same  in  principle  as 
the  transmitting  goniometer,  but  whose  coils  are  wound  with  a  different 
number  of  turns.  The  movable  coil  is  joined  to  a  detector  circuit.  A 
simple  consideration  of  the  action  of  the  transmitting  goniometer  with 
the  conditions  reversed  for  reception  makes  it  evident  that  the  receiving 
goniometer  will  respond  with  the  greatest  intensity  to  waves  approaching 

*  If  the  antennae  and  the  exciting  condenser  circuit  are  closely  coupled,  two  waves 
will  in  general  be  transmitted;  their  frequency,  however,  is  not  changed  as  the  position 
of  S  is  varied.309 


DIRECTIVE  TELEGRAPHY 


351 


in  the  direction  of  the  plane  of  the  movable  coil  and  that  it  will  fail  to 
respond  when  this  direction  is  perpendicular  to  the  approaching  waves. 
The  methods  of  BELLINI  and  Tosi  have  been  put  to  extensive  practical 
tests  in  France  and  seem  to  have  given  very  satisfactory  results.  A 
large  station  has  been  erected  on  this  principle  at  Boulogne.  The  aerials 


A' 


FIG.  423. 


are  supported  by  means  of  4  steel  towers,  are  36  m.  high,  80  m.  apart  at 
the  top  and  127  m.  apart  at  their  bases.  The  horizontal  portions  (AB, 
Fig.  418)  are  8  m.  above  the  ground  and  the  wave-length  is  300  m.  The 
Boulogne  Station  has  communicated  at  night,  using  only  0.5  kw.  energy 
with  Algiers  (1500  km.)  [See  Art.  145/  in  this  connection.] 

c.  The  distance  effect  characteristic  of  the 
double  antennae  discussed  in  a  and  b  has  the 
disadvantage  of  being  bilateral,  i.e.,  the 
effect  in  any  two  directions  180°  apart  is 
alike.  A  unilateral  characteristic  is  secured 
by  placing  a  simple  vertical  antenna  in  the 
center  of  the  pair  of  antennae  shown  in  Fig. 
418,  thereby  obtaining  the  arrangement  illus- 
trated in  Fig.  422.  If  the  current  in  this 
middle  antenna  is  in  phase  with  that  in  an- 
tenna BB',  the  effect  in  the  direction  OB  is 
strengthened,  while  that  in  direction  OA  is 
weakened;  under  suitable  conditions,  there- 
fore,  a  distance  effect  characteristic  of  the 
form  of  Fig.  423  is  obtained,  i.e.,  the  ampli- 
tude has  a  decided  maximum  in  direction  OB  and  a  decided  minimum 
in  direction  OA. 

If  it  is  desired  to  make  the  direction  of  maximum  amplitude  of  this 
arrangement  variable  at  will,  the  principle  discussed  in  b  can  be  directly 


^ 


352 


WIRELESS  TELEGRAPHY 


FIG.  425. 


applied  for  this  purpose;  to  the  radio-goniometer  with  its  two  pairs  of 
antennae  and  their  fixed  coupling  coils  S'  and  S"  (Fig.  419)  there  is  added 
a  simple  vertical  antenna  (OD,  Fig.  424)  whose  coupling  coil  is  mechanic- 
ally joined  to  the  excitation  coil  S  (Fig.  419)  and,  therefore,  turns  with  S. 
This  offers  a  simple  means  of  varying  the  direction  of  maximum  radia- 
^  tion  at  will,  the  distance  effect 

characteristic  being  of  the  form 
shown  in  Fig.  423. 

If  this  arrangement  is  used 
2  without  any  modification  as  a 

receiver  it  will  not  have  the 
same  distance  effect  character- 
istic as  it  has  when  transmit- 
ting, as  the  potential  induced 
in  the  central  vertical  antenna  would  not  be  in  phase  with  one  of  the 
inclined  antennae.  This  must  therefore  be  taken  into  consideration. 

199.  The  Methods  of  F.  Braun.311 — One  of  the  methods  with  which 
F.  BRAUN  experimented  in  1906  is  illustrated  in  Fig.  425.     The  oscilla- 
tions in  antennae  $2  and  83  are  in  phase  with  each  other,  while  those  in 
antenna  Si  are  displaced  270°  from  the  others.     The  amplitudes  in  the 
three  antennae  are  proportioned  as  follows:  AI  :Az  :AS  =  1 :0.5  :0.5;  the 

distance,  A,  between  them  is  j.  Calculating  the  values  for  the  char- 
acteristic in  this  case  (on  the  assumption  of  ground  of  very  high  con- 
ductivity), the  curve  b  of  Fig.  426 
is  obtained,  i.e.,  there  is  maximum 
radiation  in  the  direction  OA  and 
zero  radiation  in  the  opposite  direc- 
tion OB.  This  was  borne  out  in 
the  tests  made  by  the  very  strong 
effect  obtained  in  direction  OA. 
In  the  opposite  direction,  how- 
ever, the  effect,  though  very  slight, 
did  not  entirely  disappear.* 

Theoretically,  even  more  ad- 
vantageous characteristics  for 
directive  signaling  are  obtained  by 
means  of  four  antennae  suitably 
arranged  (curve  c,  Fig.  426). 

200.  Production  of  any  Desired  Phase  Difference  with  Undamped 
Oscillations  (G.  E.  PETIT312). — In  the  methods  of  BRAUN,  as  well  as 

*  In  one  test,  e.g.,  the  deflection  of  the  measuring  instrument  used  in  the  receiving 
set  was  30  scale  divisions  in  direction  OA  and  only  2  scale  divisions  in  the  opposite 
direction. 


FIG.  426. 


DIRECTIVE  TELEGRAPHY 


353 


nSTOra 


in  those  discussed  in  Art.  196c,  the  chief  difficulty  consists  in  exciting 
oscillations  of  a  certain  desired  phase  difference  in  the  transmitters.* 

This  problem  can  be  solved  very  easily,  at  least  in  principle,  in  the 
case  of  undamped  oscillations. 

An  arrangement  suitable  for  this  purpose  is  sketched  in  Fig.  427.  The 
primary  condenser  circuit  CiSiS'i,  in  which  undamped  oscillations  are 
induced  by  means  of  a  high  frequency  generator  or  the  arc  method,  acts 
inductively  (coupling  coils  Sfi  and  S'z)  upon  a  second  condenser  circuit 
CzSzS'z,  which  is  in  resonance  with  Ci/Si/S'i.  Consequently  undamped 
oscillations  are  induced  in  the  secondary  circuit  CzSzS'z,  but  these  are  90° 
out  of  phase  with  those  in  circuit  CiSiS'i* 

The  planes  of  the  two  coils  Si  and  $2  are  at  right  angles  to  each 
other.  As  the  currents  flowing  through  Si  and  82  are  90°  out  of  phase, 
a  rotating  magnetic  field  is  produced 
in  the  space  surrounding  these  coils; 
this  field  is  circular  in  form  if  the 
dimensions  and  coupling  of  the  two 
condenser  circuits  are  so  chosen  that 
the  magnetic  fields  of  each  of  the  coils 
Si  and  82  are  equal  in  amplitude.  If, 
now,  two  other  coils,  $3  and  $4,  having 
an  angle  <£  between  their  planes,  are 
inserted  in  this  rotating  field,  electro- 
motive forces,  having  a  phase  differ- 
ence <£,  will  be  induced  in  them. 
Hence,  if  $3  and  $4  are  each  connected  to  one  of  two  similar  antennae, 
the  currents  in  the  latter  will  also  have  a  phase  difference  $. 

The  amplitudes  of  the  two  antenna  currents  thus  obtained  can  also 
be  given  any  desired  ratio  by  choosing  the  number  of  turns  of  the  two 
coils  Si  and  S2  accordingly. 

201.  Production  of  any  Desired  Phase  Difference  with  Damped 
Oscillations. — This  far  more  difficult  problem  has  been  solved  by  L. 
MANDELSTAM  and  N.  PAPALEXi,313  whose  method  will  be  understood  from 
the  following  consideration. 

a.  Let  the  condenser  circuit  FC'ACLBC"F  (Fig.  428)  be  caused  to 
oscillate.  Let  V  represent  the  voltage  between  points  B  and  A,  Vi  the 
voltage  across  the  terminals  of  condenser  Ci,  Si  the  e.m.f.  induced  along 
AL'iCiU'iB.  Then,  if  the  ohmic  resistance  is  very  low,  V  =  Vi  +  8t- 
approximately. 

Vi  leads  the  current — which  is  marked  i  in  Fig.  429  and  the  following 

*  The  method  customary  in  alternating  current  practice  (light  and  power) — viz., 
branching  off  between  inductive  and  non-inductive  resistance — is  not  applicable  in 
this  case,  as  the  non-inductive  resistances  would  have  to  be  so  great  as  to  increase  the 
damping  far  beyond  permissible  limits. 
23 


rooo  01 

Si 


FIG.  427. 


354 


WIRELESS  TELEGRAPHY 


figures — by  90°  and  8;  lags  behind  the  current  by  90°.     Their  curves  are, 
therefore,  about  as  shown  in  Fig.  429. 

b.  Now  let  the  points  A  and  B  be  connected  through  a  coil  of  very 
great  self-induction.  The  rapid  oscillations  of  the  condenser  circuit  then 
continue  just  as  if  this  coil  were  not  there  [Art.  416].  But  during  the  time 
in  which  the  condenser  circuit  is  being  charged  by  the  induction  coil  (or 
transformer)  the  coil  between  A  and  B  acts  as  a  short-circuit  across  con- 


To  Induction 
Coil 


,C'      L' 


FIG.  428. 

denser,  C.     Hence,  the  potential  Vi  must  have  an  initial  value  of  zero,  and 
cannot  start  at  its  maximum  as  shown  in  Fig.  429. 

Moreover,  a  constant  potential  whose  amplitude  is  equal  to  the 
maximum  amplitude  of  the  variable  or  alternating  potential  V\  of  Fig. 
429  is  added  to  the  latter,  so  that  curves  V  and  V\  are  raised,  appearing 
as  in  Fig.  430  if  Vi0>&io)  and  otherwise  as  in  Fig.  431.  In  the  first  case, 

Vi0>&i0,  which  is  equivalent  to  stating  that  —^r>uLi}  i.e., 


when 


the 


FIG.  429. 


FIG.  430. 


condensance  of  circuit  ACiB  is  greater  than  its  inductance,  it  is  essential 
for  what  follows  that  the  maximum  of  potential  V  occurs  after  half  a  period 
of  the  condenser  circuit  FC'ACiBC"F.  In  the  second  case,  which  is  of  no 
interest  in  regard  to  what  follows,  the  maximum  of  potential  V  occurs 
immediately  after  the  beginning  of  the  oscillations. 

c.  Let  another  condenser  circuit,  77,  be  added  to  the  arrangement  of 


DIRECTIVE  TELEGRAPHY 


355 


Fig.  428,  as  shown  in  Fig.  432.  Spark  gap  FI  is  so  adjusted  in  length  that 
sparks  are  just  able  to  jump  across  it  whenever  a  spark  passes  across  F. 
Condenser  circuits  /*  and  II  are  tuned  to  be  in  resonance  with  each 
other. 

Then  if  a' spark  jumps  across  F,  condenser  circuit  II  and  condenser 
circuit  FC'ACiBC"F  will  oscillate  simultaneously.  But  the  spark  at  FI 
and,  therefore,  the  natural  oscilla- 
tions of  condenser  circuit  I  do  not 
begin  until  the  potential  Vi  at  FI 
has  reached  its  maximum,  i.e.,  until 
half  a  period  of  condenser  circuit 
FC'ACiBC"F  has  elapsed.  As  the 
natural  period  of  this  condenser 
circuit  can  be  adjusted  within  cer- 
tain limits  by  varying  the  coils 
L'L",  we  have  in  these  a  means  of 
controlling  the  time  (within  those 
limits)  which  will  elapse  before  the 
oscillations  of  condenser  circuit  / 
commence  after  those  of  circuit  II 

have  started,  i.e.,  the  means  of  giving  the  oscillations  of  circuit  I  any  desired 
phase  displacement  (within  certain  limits)  from  those  of  circuit  II. 

d.  For  carrying  this  method  out  in  practice,  the  following  points 
should  be  noted: 

1.  Above  all  the  condition  that     n  >o>Li  must  be  secured.     For  this 


FIG.  431. 


is  equivalent  to  making  the  frequency  of  condenser  circuit  FC'AC\BC"F 
less  than  that  of  condenser  circuit  /  [Art.  5a\. 


C' 

To  Induction  Coil   [I  L 


Ii 


To  Induction  Coil     n" 

FlG.  432. 


13 


2.  It  is  advantageous  to  have  the  resultant  capacity  of  condensers 
C'  and  C"  equal  to  that  of  Ci  and  of  €2,  as  this  makes  the  efficiency  of  the 
entire  system  a  maximum. 

3.  The  three  parts  into  which  the  system  divides  itself  must  have 


*  That  is 


356 


WIRELESS  TELEGRAPHY 


no  appreciable  inductive  effect  upon  one  another.  Otherwise  the  various 
reactions  which  occur  would  be  far  more  complicated  than  as  stated 
above. 

4.  To  insure  prompt  sparking  at  FI  as  soon  as  the  potential  there  is 
at  its  maximum,  it  is  advisable  to  let  the  ultra-violet  rays  from  spark 
gap  F  fall  upon  gap  FI  or  use  some  other  means  of  ionizing  gap  FI  [Art. 
426]. 

3.  AERIALS  HAVING  HORIZONTAL  OR  INCLINED  PORTIONS 

202.  Marconi's  Bent  Antenna. — MARCONI314  approached  the  prob- 
lem of  directive  signaling  in  a  way  quite  different  from  any  of  the  methods 
described  in  2. 

His  method  is  to  use  an  aerial  consisting  of  a  short  vertical  and  a  long 
jp  G  horizontal  portion,  which  in  its 

simplest  form  appears  as  shown 

433.* 

The  mere  fact  that  MARCONI 
has  shown  that,  at  a  distance 

of  about  one  wave-length,  this  transmitter  has  a  characteristic  of  the  form 
of  Fig.  434 f  proves  nothing  (according  to  Art.  92c)  in  regard  to  the  effect 
at  great  distances.  However,  MARCONI  has  demonstrated  by  means  of 
long  distance  tests,  that  this  form  of  transmitting  aerial  has  a  much 
greater  effect  in  direction  AC  than  in  the  opposite  direction  and  has  a 
particularly  small  effect  in  the  direction  perpendicular  to  the  plane  of 
the  aerial.  Hence  the  characteristic 
at  great  distances  must  also  have  a 
greater  length  (vector)  in  the  direction 
AC  than  in  the  opposite  direction. 

Fig.  43  5  J  is  a  sketch  of  the  actual 
construction  of  an  antenna  of  the  type 
of  Fig.  433,  as  used  by  MARCONI  for 
his  transatlantic  stations.  §  The  fact 


.350136 


180°  170' 
FIG.  434. 

The  direction  marked  360°  corre- 


*  When  MARCONI'S  experiments  were 
made,  it  was  found  that  the  best  results  were 
obtained  when  the  horizontal  portion  of 
the  aerial  was  one-fifth  of  the  wave-length. 
Fig.  434  is  the  characteristic  under  this  con- 
dition. 

f  From  Proc.  Royal  Soc.,  A77,  p.  415,  1906. 
sponds  to  the  direction  AC  in  Fig.  433. 

$  From  the  Jahrbuch  fur  drahtl.  Tel.,  1,  608,  1908. 

§  The  Clifden  station  is  reported315  as  having  30  masts  each  60  m.  high,  between 
which  200  parallel  wires  are  stretched  over  a  length  of  2000  m.  and  a  width  of  330  m. 
The  fundamental  wave-length  of  this  antenna  is  said  to  be  4000  m.  Later  reports 
state  that  MARCONI  now  employs  separate  transmitting  and  receiving  antennae  in  his 
transatlantic  stations.  The  transmitting  aerial  is  said  to  be  600  m.  long,  the  re- 


DIRECTIVE  TELEGRAPHY 


357 


that  MARCONI  has  adopted  this  form  for  his  transatlantic  stations  is 
perhaps  the  best  evidence  of  its  merits. 

203.  The  Action  of  the  Bent  Marconi  Antenna  when  Transmitting.— 
a.  The  action  of  the  MARCONI  antenna  can  not  be  explained  as  long  as 
we  retain  the  assumption  of  perfect  conductivity  for  the  earth. 

For  under  this  assumption  we  would  be  justified  in  replacing  the 
transmitter  of  Fig.  433  and  the  effect  of  the  earth  by  the  double  trans- 


FIG.  435. 

mitter  of  Fig.  436  without  any  ground  [Art.  138a]  and  in  calculating  the 
field  of  this  transmitter  from  the  effect  of  the  individual  current  elements 
of  the  antenna  [Art.  256],  With  a  flat  earth's  surface  the  field  in  the 
equatorial  plane  is  the  important  factor.  But  in  the  equatorial  plane 
the  fields  due  to  the  horizontal  portions  of  the  antenna  (Fig.  436)  tend 
to  neutralize  each  other  as  the  distance  from  the  transmitter  increases. 
At  very  great  distances,  which  of  course  are  always  in  question  in  wire- 


FIG.  436. 

less  telegraphy,  practically  nothing  remains  except  the  effect  of  the 
vertical  portion  of  the  antenna,  and  this  is  the  same  in  all  directions  in 
view  of  the  symmetry  of  the  vertical  portion.  Under  these  conditions, 
therefore,  this  transmitting  antenna  could  not  be  used  for  directive 
signaling. 

From  this  it  follows,  on  one  hand,  that  the  bent  MARCONI  antenna  can 
have  little  or  no  directive  power  when  located  over  sea  water,  i.e.,  on 
shipboard,*  and  would  radiate  uniformly  in  all  directions. 

On  the  other  hand,  the  directive  power  which  this  antenna  actually 
has  when  used  on  land,  can  be  explained  only  by  taking  the  action  in 

ceiving  aerial  1800  m.  long  and  only  2-4  wires  are  used.  [Translator's  Note. — The 
MARCONI  Co.  has  adopted  separate  transmitting  and  receiving  stations  for  all  its  new 
transatlantic  stations,  as  e.g.,  New  Brunswick  and  Belmar.] 

*  Or  rather,  to  be  more  exact,  on  a  wooden  raft;  for  the  metal  rigging  of  a  modern 
ship  affects  the  radiation  and  destroys  its  uniformity. 


358  WIRELESS  TELEGRAPHY 

the  ground  and  the  latter's  conductivity  and  dielectric  constants  into 
consideration. 

b.  The  first  real  explanation  of  the  bent  MARCONI  antenna  was  given 
comparatively  recently  by  H.  VON  HoERSCHELMANN,316  a  pupil  of  A. 
SOMMERFELD.  His  theory,  based  on  the  assumption  of  homogeneous 
ground  in  the  vicinity  of  the  transmitter  in  both  horizontal  and  vertical 
directions  may  be  developed  as  follows : 

The  action  of  a  horizontal  antenna  stretched  out  over  ground  of  mod- 
erate conductivity,  consists  in  its  inducing  powerful  earth  currents 
in  its  immediate  vicinity  in  the  upper  strata  of  the  earth.  The  amplitude 
of  the  vertical  components  of  these  currents  has  a  sharply  defined  maxi- 
mum at  a  certain  distance  to  either  side  of  the  middle  of  the  antenna 
(in  the  plane  of  the  antenna)  and  the  phases  of  the  vertical  component 
currents  to  the  right  and  to  the  left  of  the  middle  point  are  opposite. 
In  accordance  with  the  theory,  we  may  now  consider  all  the  vertical 
components  of  the  earth  currents  as  being  concentrated  at  the  two 
maximum  points  mentioned  above  and  the  entire  action  then  pro- 
ceeds as  if  two  simple  wave  series  were  being  radiated  from  two  vertical 
antennae  erected  at  the  two  points  of  maximum  and  whose  currents 


J"' 

1 

I 

r 

u 

! 

1 
I 

II 

!, 

\o 

U 

A 

FIG.  437. 

were  opposite  in  phase.  This  imaginary  vertical  double  antenna  in  short 
is,  so  to  say,  automatically  produced  in  the  ground  by  the  horizontal  trans- 
mitting antenna. 

The  field  of  the  bent  MARCONI  antenna  as  can  be  shown  from  the  theory, 
is  easily  calculated  by  superimposing  the  field  of  the  vertical  portion  A B 
(Fig.  437)  upon  that  of  the  two  imaginary  antennae  XX'  and  YY'  pro- 
duced by  the  horizontal  portion  BC,  both  being  calculated  according 
to  the  rules  of  Art.  25,  just  as  if  the  conducting  earth  were  not  present. 

This  system  of  antennae  therefore  resembles  the  arrangement  dis- 
cussed in  Art.  198c,  the  combination  of  a  simple  vertical  antenna  with  a  pair 
of  antennoB  oscillating  in  opposite  phases.  But  in  the  case  before  us 
the  distance  d  =  XY  between  the  pair  of  antennae,  is  not  optional, 
being  in  fact  equal  to  the  height  h  (  =  AB  Fig.  437)  of  the  MARCONI 
antenna.  Moreover,  the  phase  of  the  oscillations  in  the  double  antenna 
is  not  the  same  as  (nor  opposite  to)  that  of  the  oscillations  in  antenna 
A  B,  but  the  oscillations  in  XX'  lag  45°  behind  those  in  AB.  Finally, 
the  amplitudes  of  the  waves  radiated  by  each  of  the  imaginary  pair 


DIRECTIVE  TELEGRAPHY  359 

of  antennae  XX'  and  YY'  though  equal  to  each  other,  are  not  equal  to 
the  amplitude  of  the  wave  radiated  by  antenna  AB.  Denoting  the 
former  amplitude  by  Efo  and  the  latter  by  Eho,  their  relation  is  given  by* 

(1) 

The  two  imaginary  antennae  according  to  Art.  1966  produce  a  field 
whose  amplitude  at  a  very  distant  point  P*  is 

E'Q  =  2Efo  ~  cos  X  =  2Efo  •  ~  cos  tff  (2) 

A  A 

If  we  superimpose  the  wave  radiated  by  this  imaginary  double  antenna 
upon  that  radiated  by  the  vertical  antenna,  keeping  the  45°  difference  in 
phase  in  mind — we  obtain  the  amplitude  of  the  resultant  wave, 

(3) 
=  tiho  \1 +0*008* #+ V^.jS cos  #J 

7  1 

in  which 


2crXc 

This  relation  determines  the  distance  effect  characteristic  of  the 
bent  transmitting  antenna.  Its  form  depends  upon  the  value  of  /3,  i.e., 
aside  from  the  wave-length,  it  depends  mainly  upon  the  ratio  of  the 
length  of  the  horizontal  portion  of  the  antenna  to  the  vertical  portion 
and  upon  the  conductivity  of  the  ground.  In  Fig.  438  the  distance 
effect  characteristics  are  shown  for  @  =  4{  (heavy  full  line  curve  6) 
and  for  /?  =  1.4§  (lighter  curve  c);  they  correspond  to  ground  of  poor 
conductivity.  The  former,  6,  is  very  similar  to  that  observed  experi- 
mentally by  MARCONI  (Fig.  434) ;  the  theory  therefore  gives  results  which 
agree  well  with  the  actual  facts.  The  maximum  directive  power  is 
obtained  when  /3  =  1  (characteristic  very  similar  to  curve  c) ;  with  $  = 
0.2  the  characteristic  (dot-and-dash  curve  d,  Fig.  438)  has  already  lost 
its  directive  form  to  a  very  large  extent. 

If  the  conductivity  of  the  ground  is  very  great,  making  (3  very  small, 
then,  in  equation  (3)  the  first  term  under  the  radical  sign  becomes 

*  Under  the  following  assumptions : 

1.  Height,  h,  and  length,  I,  of  the  antenna <^X. 

2.  The  expression  —j—  ^1.0    [where   a-  =  specific    conductivity  of   the  ground, 

VL  =  velocity  of  light  and  k  =  dielectric  constant  of  the  ground,  all  in  c.g.s.  units]. 
This  assumption  is  always  correct  for  the  conditions  encountered  in  practice. 
t  $POA  =  &  [see  Art.  196]. 
J  Corresponding,  e.g.,  to  :  a  =  1.2  X  10~16  c.g.s.  units; 

X  =  2000  m.; 
l/h  =  5. 
§  Corresponding,  e.g.,  to  :  er  =  10~15  c.g.s.  unitsj 

X  =  2000  m.  ; 
l/h  =  5. 


360 


WIRELESS  TELEGRAPHY 


the  determining  factor  and,  as  was  to  be  expected  from  a,  Er<t  becomes 
equal  to  Eh0,  i.e.,  the  distance  effect  becomes  virtually  identical  with 
that  of  the  vertical  portion  AB  (Fig.  438,  curve  e).  In  the  other  limiting 
case,  if  0  is  very  great — say  the  horizontal  portion  is  very  much  longer 
than  the  vertical  part  of  the  antenna — the  effect  of  the  horizontal  por- 
tion predominates  and  the  form  of  the  characteristic  approaches  that  of 
a  pair  of  antennae  with  currents  of  opposite  phase  (Fig.  438,  curve  a; 
compare  Fig.  410),  i.e.,  the  antenna  radiates  about  equally  in  directions 
AB  and  AC  of  Fig.  433,  but  only  very  slightly  in  the  direction  per- 
pendicular to  AB  and  AC. 

c.  It  follows,  therefore,  that  in  order  to  operate  directively,  the  bent 
MARCONI  antenna  must  be  placed  over  ground  of  low  conductivity; 


FIG.  438. 

the  directive  power  is  the  result  of  the  earth  currents.  In  this  respect 
then  the  bent  antenna  differs  fundamentally  from  the  arrangements 
employing  several  antennae  with  currents  displaced  in  phase,  as  dis- 
cussed in  1.  The  latter  have  directive  power  no  matter  what  the  nature 
of  the  ground,  retaining  it  even  when  used  on  shipboard  over  sea  water. 
However,  with  the  bent  MARCONI  antenna  it  suffices  if  ground  of  low 
conductivity  surrounds  the  antenna  for  only  a  comparatively  short 
radius  to  secure  the  directive  power.  It  seems  that,  once  the  waves 
have  developed  a  directive  distribution  in  the  vicinity  of  the  transmitter, 
they  will  retain  this  in  passing  over  ground  of  high  conductivity,  as  in 
traveling  over  sea,  later  on.  In  regard  to  the  propagation  of  directed 
waves,  the  same  conditions  (absorption,  direction  of  the  field  at  the 


DIRECTIVE  TELEGRAPHY 


361 


earth's  surface)  hold  as  for  waves  radiated  uniformly  in  all  directions 
[Art.  139  et  seq.]. 

204.  The  Bent  Marconi  Antenna  used  for  Receiving.317 — a.  In  his 
long  distance  experiments,  MARCONI  found314  that  his  antenna  responded 
far  better  to  waves  approaching  in  the  direction  of  the  arrow  in  Fig. 
439  than  to  waves  traveling  in  the  opposite  direction;  the  effect  of 
waves  approaching  in  a  direction  perpendicular  to  the  plane  of  the 
antenna  was  intermediate  between  that  of  the  other  two  extreme  cases. 

In  other  tests  that  were  made  the  difference  between  the  effect  of 
waves  having  the  direction  of  the  arrow  in  Fig.  439  and  waves  having  the 


FIG.  439. 

opposite  direction  was  but  very  slight;  but  waves  approaching  per- 
pendicularly to  the  plane  of  the  antenna  had  only  very  little  effect  in 
comparison. 

6.  No  complete  explanation  of  the  action  of  the  bent  MARCONI  antenna 
when  receiving  has  been  given  to  date.  Not  only  the  effect  of  the 
electromagnetic  waves  in  the  air  upon  the  horizontal  and  vertical  por- 
tions of  the  antenna,  but  also  the  effect  of  the  field  of  the  waves  in 
the  earth  upon  the  earth  currents,  which  according  to  Art.  203  form  a 
material  part  of  the  natural  oscillations  of 
these  antennae,  would  have  to  be  considered 
in  seeking  an  explanation.  If  it  were  possi- 
ble in  this  case  to  substitute  the  action  of 
two  imaginary  antennae  for  that  of  the 
earth  field,  as  was  done  in  Art.  2036,  the 
problem  would  become  relatively  simple. 
This  substitution,  however,  is  not  clearly 
justified  in  this  case. 

A  qualitative  explanation  of  the  action  of  the  bent  antenna  when 
receiving,  as  found  from  the  test,  can  be  obtained  by  simply  considering 
the  effect  of  the  field  in  the  air  upon  the  horizontal  and  vertical  portions  of 
the  aerial  proper  (J.  ZENNECK317). 

1.  In  order  to  simplify  the  conditions  involved  as  much  as  possible, 
let  us  first  assume  that  the  electrical  field  produced  by  the  transmitted 
waves  is  an  alternating  field  whose  direction  is  inclined  at  a  considerable 
angle  to  the  vertical  direction  [Art.  139e].  Let  this  direction  be  that  of  E 
in  Fig.  440.  EI  and  E%  are  respectively  the  vertical  and  horizontal 
components  of  the  electric  field  strength.  The  potential  difference 
produced  in  the  antenna  by  this  field  is  made  up  of  the  potential  along 


362 


WIRELESS  TELEGRAPHY 


AG  (Fig.  441),  which  is  produced  entirely  by  the  vertical  component,  EI, 
and  that  along  GH,  which  is  produced  solely  by  the  horizontal  component, 
E2.  As,  under  our  assumption,  the  vertical  and  horizontal  components 
are  in  phase,  the  potentials  across  AG  and  GH  are  added,  i.e.,  the  ampli- 
tude of  the  potential  difference  along  the  entire  antenna  AGH  =  the  sum 
of  the  amplitudes  of  the  potential  differences  induced  in  the  horizontal 
and  vertical  portions  of  the  antenna. 


But  if  the  antenna  is  turned  through  an  angle  of  180°,  as  shown  in 
Fig.  442,  then  the  amplitude  of  the  total  potential  difference  along  AGH  — 
the  difference  between  the  potentials  induced  in  the  vertical  portion,  AG, 
and  the  horizontal  portion,  GH. 

Finally,  if  the  receiving  antenna  is  so  placed  that  its  plane  is  perpen- 
dicular to  the  direction  of  propagation  of  the  waves,  the  horizontal  com- 
ponent, EZ,  has  no  effect  at  all  and  only  the  effect  upon  the  vertical 
portion,  AG,  remains. 

We  can  distinguish  between  two  general  cases: 

a.  The  potential  induced  in  the  horizontal  portion,  GH,  is  smaller 
than  that  induced  in  the  vertical  part,  AG.  Then,  from  what  has  pre- 


FIG.  442. 

ceded,  it  follows  that  the  incoming  wave  must  have  a  maximum  effect 
upon  the  receiver  in  the  position  of  Fig.  441,  a  minimum  in  that  of 
Fig.  442  and  effects  intermediate  between  these  limits  when  the  plane 
of  the  antenna  is  perpendicular  to  the  direction  of  the  approaching 
waves. 

/3.  The  potential  induced  in  the  horizontal  portion  is  considerably 


DIRECTIVE  TELEGRAPHY 


363 


greater  than  that  induced  in  the  vertical  part.  Then  the  effects  for  the 
two  positions  of  Figs.  441  and  442  will  differ  only  slightly,  but  will  be 
greatly  reduced  when  the  antenna  plane  is  perpendicular  to  the  direction 
of  the  approaching  waves. 

2.  If  the  electric  field  at  the  surface  of  the  earth  is  not  a  pure  alternat- 
ing field,  but  has  a  more  or  less  prominent  rotating  component  [Art.  139e], 
then  the  horizontal  and  vertical  components  of  the  field  are  no  longer  in 
phase.  However,  as  this  phase  difference  lies  between  0  and  45°,  the 
results  of  1  remain  qualitatively  unchanged.  But  the  difference  in  the 
effects  obtained  in  the  two  chief  positions  (Figs.  441  and  442)  becomes  less 
and  less  as  this  phase  difference  increases. 

c.  The  characteristic  of  this*  type  of  directive  receiving  antenna  de- 
pends upon  the  relation  of  the  effect  upon  the  horizontal  portion  to  the 
effect  upon  the  vertical  portion.  This  in  turn  depends  upon: 

1.  The  ratio  of  the  length  of  the  horizontal  to  that  of  the  vertical 
portion  of  the  antenna. 

2.  The  nature  of  the  ground,  inasmuch  as  this  determines  the  am- 
plitude ratio  of  the  vertical  and  horizontal  field  components  as  well  as  the 
phase  displacement  between  these  components  [Art.  139e], 

If  the  antenna  is  located  over  sea  waterj  the  effect  produced  upon  it 
can  depend  very  little,  if  at  all,  upon  the  position  (direction)  of  the  an- 
tenna; in  short  it  is  no  longer  directive.  For  in  this  case,  according  to 


Art.  138c,  the  horizontal  field  component  vanishes  to  an  infinitesimal 
value  as  compared  to  the  vertical  component,  so  that  the  effects  upon  the 
horizontal  and  vertical  parts  of  the  antenna  bear  the  same  relation  to 
each  other. 

205.  Inclined  Antennae. — a.  As  early  as  1902,  F.  BRAUN,311  conducted 
successful  experiments  with  an  antenna  of  the  form  shown  in  Fig.  443 
(AB  is  the  antenna,  C  is  a  condenser  circuit  tuned  to  it  and  directly 
coupled  with  it).  The  angle  between  the  antenna  and  the  horizontal 
earth's  surface  was  about  5°.  It  was  found  that  this  form  of  receiving 

*  Other  types  of  directive  receiving  antenna  can  be  explained  in  a  similar  manner. 

t  If  the  antenna  is  on  board  a  ship,  the  metallic  masses  of  the  latter  are  apt  to 
cause  considerable  distortion  of  the  electric  field,  so  that  the  simple  conditions  assumed 
above  no  longer  hold  true. 


364  WIRELESS  TELEGRAPHY 

antenna  responded  with  the  greatest  intensity  to  waves  traveling  in  the 
vertical  plane  passing  through  the  antenna  and  was  only  very  slightly 
affected  by  waves  approaching  in  a  direction  perpendicular  to  this  plane. 

b.  Since  these  early  experiments,  frequent  observations  have  been 
made  in  practice  of  the  fact  that,  e.g.,  harp  or  fan-shaped  antennae  which 
are  suspended  at  an  angle  from  the  two  towers  which  support  them,* 
respond  much  better,  when  receiving,  to  waves  having  the  direction  of  the 
arrow  in  Fig.  365  than  to  waves  approaching  in  other  directions  and 
when  transmitting,  the  amplitude  of  the  waves  radiated  is  greatest  in  the 
direction  opposite  to  that  of  the  arrow  in  Fig.  365. 

c.  An  explanation  of  the  directive  power  of  these  antennae  when  re- 
ceiving can  at  once  be  found  in  the  fact  that  for  waves  traveling  along 
ground  of  low  conductivity,  the  direction  of  the  electric  field  instead  of 
being  vertical,  is  inclined  toward  the  earth's  surface  [Art.  139e]  and  that 
any  antenna  must  respond  to  the  greatest  extent  when  its  direction  coin- 
cides with  that  of  the  field  acting  upon  itf  [Art.  171]. 

The  directive  power  of  these  inclined  antennas  when  transmitting  can 
probably  be  explained  similarly  to  that  of  the  bent  MARCONI  antenna  when 
transmitting.  We  may  assume  that  the  distance  effect  of  an  antenna 
current  inclined  to  the  earth's  surface  can  be  split  up  into  the  respective 
effects  of  a  vertical  and  a  horizontal  component  current. 

From  the  preceding  it  would  be  expected  that  the  directive  power  of 
inclined  antennae,  both  when  transmitting  and  receiving,  vanishes  when 
they  are  located  over  ground  of  very  high  conductivity. 

206.  Horizontal  Antennae,  Ground  Antennas. — In  the  experiments 
of  F.  BRAUN  (Art.  205a),  the  slight  inclination  of  the  antenna  toward 
the  horizontal  (Fig.  443)  was  of  no  material  importance.  Undoubtedly 
BRAUN  would  have  obtained  about  the  same  results  if  the  antenna  had 
been  exactly  horizontal. 

Such  horizontal  antennae,  which  differ  from  the  bent  MARCONI  antenna 
in  consisting  of  two  symmetrical  halves  at  a  slight  distance  above  the  ground, 
have  recently  been  termed  "ground  antennae".318  They  have  been 
proposed  by  many  others  (e.g.,  by  MARCONI,  L.  ZEHNDER318)  besides 
BRAUN  and  have  been  tried  out  here  and  there.  The  general  opinion 
seems  to  have  been  though  that  their  effectiveness  was  so  far  below  that 
of  vertical  antennae  as  to  eliminate  them  from  practical  use.  In  recent 
times,  however,  F.  KiEBiTZ318  has  shown  that  considerable  ranges  can  be 
attained  with  these  antennae.  Thus  with  a  receiving  aerial  240  m.  long 
at  Belzig,  the  signals  of  the  station  on  the  Admiralty  Office  in  London  could 
be  clearly  received  (distance  880  km. ;  horizontal  portion  of  receiving  an- 

*  As  for  instance  the  antenna  of  the  Eiffel  Tower. 

f  This  by  no  means  applies  to  the  antenna  of  Fig.  443;  for  its  angle  with  the  hori- 
zontal is  so  small  that  it  comes  mainly  under  the  influence  of  the  horizontal  field 
component. 


DIRECTIVE  TELEGRAPHY  365 

tenna  1  m.  above  ground).  Messages  from  the  same  antenna  when 
transmitting  were  easily  received  at  Swinemiinde,  230  km.  away.* 

The  antennae  used  by  KIEBITZ  consisted  either  of  two  free  ended 
halves  like  that  of  BRAUN  (Fig.  443),  or  each  half  was  grounded  at  its 
end,  A  and  B  (Fig.  444)  through  a  condenser. 

The  action  of  these  antennae  (i.e.,  their  horizontal  part)  can  un- 
doubtedly be  replaced,  at  least  approximately,  by  the  action  of  a  pair  of 
vertical  antennae  whose  currents  are  equal  in  amplitude  but  opposite  in 
phase,  according  to  Art.  2036.  f  Thej^  must  transmit  the  maximum 


r-—-  ------  msm^ 

'''    '  '  ' 


FIG.  444. 

energy  in  the  vertical  plane  passing  through  them  and  must  receive  with 
the  greatest  intensity  waves  whose  direction  of  travel  is  in  this  vertical 
plane. 

Such  tests  as  have  been  made  to  date  are  not  yet  complete  enough  to 
permit  the  formation  of  any  final  conclusions  as  to  the  comparative  rela- 
tions between  horizontal  and  vertical  antennae.  Nevertheless  it  would 
seem  safe  to  conclude  from  the  results  already  obtained,  that  in  certain 
special  cases  the  vertical  antenna  can  be  efficiently  replaced  by  the 
horizontal  ground  antenna. 

207.  The  Advantages  of  Directive  Signaling.  —  a.  Directive  Trans- 
mitters. —  If  the  problem  of  directive  signaling  were  solved,  i.e.,  if  we  had 
a  transmitter  which  would  radiate  almost  entirely  in  a  single  given 
direction,  the  following  advantages  would  be  secured. 

1.  In  radio-telegraphy  at  present  only  that  portion  of  the  energy  which 
is  transmitted  in  the  direction  of  the  receiver  appears  to  be  useful.     It 
follows  that  a  directive  transmitter,  operating  at  the  same  efficiency  (at 
the  transmitter),  would  give  the  maximum  amount  of  useful  energy.319 

2.  A  directive  transmitter  would  accomplish  a  great  step  forward  in 
securing  secrecy  of  messages.     Assume  SA  (Fig.  445)  to  be  the  range  of 
transmitter  S  for  a  given  receiver  E.     If  the  transmitter  is  non-directive, 
E  will  be  able  to  receive  its  signals  anywhere  within  the  circle  drawn  in 
Fig.  445.     But  if  the  transmitter  is  directive  and  has  a  characteristic  as 
shown  by  the  heavy  line  curve  in  the  figure   (which  represents  high 

*  In  fact  some  of  the  signals  from  the  MARCONI  station  at  Glace  Bay  (Canada) 
seem  to  have  been  received  with  a  low  horizontal  antenna  about  1200  m.  long. 

f  However,  the  various  relations  governing  the  amplitude  of  the  oscillations  in  the 
two  imaginary  antennae  and  the  distance  between  them  as  given  in  Art.  2036  can 
be  applied  to  the  present  case  only  if  the  length  of  the  horizontal  portion  is  small 
compared  to  the  wave-length  (see  foot-note,  Art.  2036). 


366 


WIRELESS  TELEGRAPHY 


directive  power),  then  E  must  be  within  the  small  shaded  area  to  receive 
the  signals  from  S. 

3.  For  the  same  reasons,  it  is  evident  that  with  directive  transmitters 


FIG.  445. 

interference  between  various  stations  operating  in  the  same  zone  is  greatly 
reduced. 

b.  Directive    Receivers. — 1.  Interference    between    neighboring    stations 
can  be  reduced  to  an  even  much  greater  extent320  if  directive  receivers  are 


T 


FIG.  446. 


FIG.  447. 

employed,  that  is  if  the  receivers  respond  almost  solely  to  waves 
approaching  in  the  direction  of  the  transmitting  station  with  which 
communication  is  intended. 

2.  Operation  with  directive  receivers  offers  another  advantage.     If  a 


DIRECTIVE  TELEGRAPHY  367 

station  is  equipped  with  two  directive  receivers,  EI  and  E2  (Fig.  446), 
each  of  which  is  differently  directed,  then  messages  can  be  received 
simultaneously  from  two  different  transmitters,  Si  and  $2,  even  if  these 
operate  at  the  same  wave-length. 

This  may  be  an  important  advantage  in  case  both  transmitting  stations 
are  obliged  to  operate  at  the  same  normal  wave-length  (as,  e.g.,  two  light- 
ship stations)  due  to  their  both  working  with  stations  for  which  a  definite 
wave-length  is  specified  (e.g.,  the  ships  of  a  fleet  or  the  merchant  marine). 

3.  Finally,  the  directive  receiver  offers  a  means  of  determining  the 
direction  in  which  the  transmitter  is  located. 

For  this  purpose,  it  would  only  be  necessary  theoretically — in  practice 
this  would  involve  great  difficulties — to  turn  the  receiver  about  a  vertical 
axis;  then  the  direction  of  the  transmitter  would  be  that  in  which  the 
receiver  responds  with  the  greatest  intensity. 

Another  method  would  be  to  have  a  complete  circle  of  directive  re- 
ceivers (Fig.  447).  Then  if  receiver  EA  is  the  only  one  to  respond,  or  at 
least  responds  with  maximum  intensity,  the  transmitter  must  lie  in  direc- 
tion ES.  Thus  if  such  a  station  is  erected  on  land  and  a  message  is 
received  by  it  from  a  ship  at  sea,  this  gives  an  immediate  indication  of 
the  direction  of  the  ship.  MAKCONI  made  a  number  of  experiments  along 
this  line;  it  was  found  possible  to  determine  with  considerable  accuracy 
the  direction  of  ships  about  90  km.  from  shore.321 

The  BELLINI  and  Tosi  apparatus*  are  particularly  convenient  for  this 
purpose.  The  receiving  radio-goniometer  [Art.  1986]  offers  a  direct 
means  of  determining  the  direction  of  approaching  waves.  The  movable 
coil  of  the  radio-goniometer  is  rotated  until  the  signals  in  the  receiver  have 
their  maximum  intensity.  As  this  maximum  is  not  very  sharp  (see 
characteristics  in  Figs.  410  and  423),  more  exact  results  are  obtained  by 
finding  the  position  of  the  movable  coil  in  which  the  received  signals 
vanish  or  have  minimum  intensity;  the  direction  of  the  approaching 
waves  is  then  perpendicular  to  this  position  of  the  coil. 

But  if  the  waves  must  travel  over  land  for  considerable  distances 
none  of  these  methods  can  be  counted  upon.  For  in  that  case,  the 
assumption  that  the  direction  in  which  the  waves  approach  the  receiver 
is  the  same  as  that  in  which  the  transmitter  is  located  with  respect  to  the 
receiver,  is  not  necessarily  correct  [Art.  143a]. 

c.  Another  problem  in  directive  radio-signaling,  which  has  recently 
gained  in  importance  is  the  following:  Given  two  fixed  land  stations  of 
known  location  and  a  moving  station  (ship,  balloon,  aeroplane);  to  de- 
termine the  location  of  the  latter  at  any  instant.™* 

*  They  seem  to  be  giving  very  good  results.  BELLINI  and  Tosi  claim  that  by  means 
of  the  antennae  described  in  Art.  198c  (combination  of  symmetrical  and  double 
antenna)  the  direction  can  be  determined  within  1°.  P.  BRENOT  reports  that  the 
direction  of  ships  300  km.  away,  could  be  determined  within  4°  to  5°.322 


368  WIRELESS  TELEGRAPHY 

1.  One  solution  is  to  equip  the  moving  station  with  a  directive 
receiver  and  by  means  of  this  determine  the  direction  of  approach  of  the 
waves  from  each  of  the  fixed  stations.  The  BELLINI  and  Tosi*  method 
is  well  suited  for  such  receivers,  while  the  double  antenna,  with  the 
two  antennae  half  a  wave-length  apart,  seems  well  adapted  for  use  on 
dirigible  balloons  [Art.  96a  (4)].  These  methods,  however,  involve 
considerable  practical  difficulties,  particularly  because  they  are  suitable 
for  short  wave-lengths  only,  so  that  a  separate  receiver  becomes  necessary 
for  the  longer  waves  used  in  regular  service. 

f  2.  A  second  solution  of  the  problem  is  as  follows:  The  fixed  stations 
are  provided  with  a  directive  receiver.  The  moving  station  must  then 
call  the  fixed  stations  to  determine  its  own  position.  The  latter  then 
each  find  the  direction  from  which  the  waves  radiated  by  the  moving 
station  come  in,  and  inform  the  moving  station  of  this  direction.  In  this 
case  of  course  the  moving  station  does  not  require  directive  apparatus 
for  either  transmission  or  reception. 

3.  Another  solution  was  proposed  some  time  ago  by  A.  AnTOM324a  and 
was  tried  out  later  by  the  Prussian  Ministry  of  Public  Works.  Each  of 
the  two  fixed  stations  is  provided  with  a  set  of  directed  transmitting 
antennae  by  means  of  which  waves  can  be  radiated  in  any  one  of  various, 
say  16,  different  directions.  The  fixed  stations  radiate  some  signals 
(different  for  the  two  stations,  as,  e.g.,  two  different  letters)  in  each  of  the  16 
directions  consecutively.  The  moving  station,  which  is  equipped  with  an 
ordinary  non-directive  receiver,  determines  which  signal  comes  in  with 
the  greatest  intensity.  Thus  if,  e.  g.}  this  is  the  letter  "  a  "  and  the  moving 
station  knows  that  this  "a"  is  being  sent  out  from  the  south-north  trans- 
mitter of  one  of  the  fixed  stations,  the  operator  at  the  moving  station 
concludes  that  he  is  in  a  direction  north  from  that  fixed  station.  The 
direction  with  respect  to  the  other  fixed  station  is  then  determined  in  a 
similar  manner. 

In  the  tests  made  near  Berlin,  32  masts  were  erected  at  the  transmit- 
ting station  in  a  circle  of  about  200  m.  diameter.  Each  mast  supported 
an  aerial,  and  the  aerials  of  each  pair  of  diametrically  opposite  masts  were 
joined  by  a  horizontal  conductor.  As  the  latter  was  approximately  equal 
to  half  a  wave-length,  each  pair  of  antennae  comprised  a  radiating  system 
of  the  type  described  in  Art.  197a.  The  station  building  was  located  at 
the  center  of  the  circle,  where  the  16  double  antennae  could  be  con- 
veniently coupled  with  the  primary  circuit,  one  after  another. 

This  method  has  been  recently  developed  by  A.  MEISSNER  (TELE- 
FUNKEN  Co.324)  into  a  commercial  form  of  apparatus  (the  "  Telefunken 
Compass'').  The  directive  transmitting  antennae,  CBABid  (Fig. 

*  BELLINI  and  Tosi  have  devised  a  compass  system,  for  use  in  the  vicinity  of  ports, 
by  means  of  which  incoming  ships  can  find  the  entrance  to  the  harbor  through  heavy 
fog  (low  power  transmitter  having  15  to  20  miles  range).323 


DIRECTIVE  TELEGRAPHY 


369 


448),  which  are  placed  radially  about  the  building  of  the  fixed  station  A, 
are  combinations  of  two  bent  MARCONI  aerials.  They  are  all  supported 
by  a  single  central  mast,  which  also  carries  a  non-directive  umbrella 


A 

FIG.  448. 

aerial,  ADEiE.  By  means  of  an  automatic  contactor  (Fig.  449  shows 
the  contact  device  with  its  driving  motor  and  the  contact  points  of  the 
different  antennae  .at  the  top)  first  the  umbrella  aerial  (time  signal) 
and  then  each  of  the  directive  antennae  are  in  turn  connected  to  the 
primary  circuit  at  given  equal  intervals  for  excitation. 


FIG.  449. 

The  moving  station  is  provided  with  a  stop-watch,  of  the  form  shown 
in  Fig.  450,  whose  pointer  makes  one  complete  revolution  in  the  same  time 
(J-2  minute)  which  the  contactor  takes  to  connect  all  of  the  directive 

•    24 


370 


WIRELESS  TELEGRAPHY 


transmitting  antenna  pairs  once  in  turn.  At  the  instant  when  the 
operator  of  the  moving  station  hears  the  time  signal  (z,*  Fig.  450),  he 
presses  his  stop-watch  and  sets  it  going.  He  then  stops  it  at  the  moment 
when  the  incoming  signals  are  loudest  ;f  then  the  position  of  the  stop- 
watch pointer  indicates  the  direction  of  that  one  of  the  double  antennae 
of  the  fixed  station  which  is  in  line  with  the  moving  station  at  that  in- 


FIG.  450. 

stant.  If  this  procedure  is  repeated  several  times  and  the  average  of 
the  stop-watch  pointer  positions  noted,  the  direction  can  be  determined 
within  4°  to  5°. 

In  tests  made  with  a  mast  23  m.  high  and  using  about  0.5  kw.  energy 
the  direction  of  a  balloon  from  the  compass  station  was  determined  quite 
accurately  up  to  a  distance  of  100  km. 

*"z"  is  not  shown  in  cut,  but  refers  to  point  between  31  and  1  on  the  watch 
scale. 

f  As  the  maximum  intensity  is  usually  not  very  sharply  denned,  it  is  probably 
better  to  determine  the  position  of  minimum  intensity. 


CHAPTER  XIV 
WIRELESS  TELEPHONY325 

1.  THE  TRANSMITTER 

208.  Source  of  Energy. — Very  soon  after  the  earliest  successes  in 
wireless  telegraphy,  attempts  were  made  to  transmit  speech  by  means  of 
electromagnetic  waves. 

a.  As  long  as  damped  oscillations  with  relatively  low  discharge  fre- 
quency were  employed,  the  results  of  such  tests  necessarily  remained 
unsatisfactory.     The   essential   requirement   for   good   transmission   of 
speech  seems  to  be  a  discharge  frequency  considerably  higher  than 
the  highest  frequency  of  the  tones  used  in  speech. 

Accordingly,  only  those  methods  which  permit  the  use  of  very  high 
discharge  frequencies  [Art.  Ill]  come  into  consideration  here.  And 
with  these  methods  fair  results  have  been  obtained  by  many  investigators 
(FESSENDEN,  AUSTIN,  v.  LEPEL  and  MAJORANA321)  some  of  whom  used 
discharge  frequencies  as  high  as  10,000  per  second.  Even  to  the  present 
day  W.  DuBiLiER326  seems  to  be  working  with  quenched  gap  transmitters, 
though,  to  be  sure,  he  employs  extremely  high  discharge  frequencies. 

b.  Undamped  oscillations,  however,  are  by  far  more  advantageous 
for  radio-telephone  work.     From  the  very  first  R.  A.  FESSENDEN  sought 
a  practical  solution  of  the  problem  along  these  lines,  producing  the  un- 
damped oscillations  by  means  of  a  high  frequency  alternator.     His  first 
alternator  operated  at  80,000  cycles  per  second  (X  =  3750  m.)  and  was 
of  1  kw.  capacity.     Even  as  early  as  1904  the  NAT.  ELEC.  SIG.  Co.,  with 
which  FESSENDEN  was  associated,  guaranteed  to  establish  wireless  tele- 
phone communication  over  a  distance  of  25  miles  (according  to  MR. 
FESSENDEN). 

POULSEN  also  promptly  used  his  arc  generator  for  wireless  telephony; 
he,  as  well  as  others,  e.g.,  A.  F.  COLLINS,  M.  COLIN  and  R.  JEANCE326 
seem  to  have  spent  considerable  effort  in  developing  this  phase  of  the 
work.  The  POULSEN  stations  in  California  have  a  range  of  550  km., 
using  ordinary  microphones  and  with  an  antenna  94  m.  high.327  The 
clearness  of  the  reproduction  of  the  transmitted  sounds  in  the  receiver 
has  been  praised  in  every  test. 

209.  Connectors. — a.     Wireless   telephone  transmitters  all  have  a 
microphone  into  which  is  spoken.     This  microphone  is  usually  connected 
in  such  a  manner  that  its  resistance  variations,  which  follow  the  oscilla- 
tions of  the  impressed  sound  waves,  cause  corresponding  variations  in 
the  amplitude  of  the  radiated  waves. 

371 


372 


WIRELESS  TELEGRAPHY 


FIG.  451. 


This  can  be  accomplished  in  a  great  variety  of  ways.  The  micro- 
phone can  be  inserted  directly  in  the  antenna,  or  with  a  coupled  trans- 
mitter, in  the  primary  circuit,  or  in  the  current  supply  circuit,  or,  finally, 
in  the  excitation  circuit  of  the  POULSEN  arc  field  magnets,  or  the  field 
circuit  of  the  high  frequency  generator.  Moreover  it  is  not  necessary 
that  the  microphone  be  inserted  directly  in  any  of  these  circuits;  it  can 
be  placed  in  a  separate  circuit  and  the  latter  then  be  coupled  to  the 

particular  circuit  which  is  to  be  affected 
by  the  action  of  the  microphone.  All 
these  theoretical  possibilities  have 
been  described  as  " inventions"  in 
patent  papers. 

The  arrangement  most  extensively 
used  in  actual  practice  is  that  of 
PouLSEN328 — a  coupled  transmitter  and 
the  microphone,  or  microphones,  (Mt 
Fig.  451)  inserted  directly  in  the  an- 
tenna. With  this  arrangement  the 
coupling  between  the  primary  circuit 
and  the  antenna  should  be  as  loose 
as  possible. 

In  the  arrangement  of  Fig.  451,  as 

well  as  in  the  commercial  form  of  this  method  shown  at  the  right  of  Fig. 
452,  several  microphones  are  used,  all  joined  to  a  common  mouthpiece. 
The  object  of  this  is  mainly  to  make  full  use  of  the  energy  of  the  sound 
waves  much  of  which  would  be  lost  with  only  a  single  microphone. 

However,  the  use  of  several  microphones  connected  in  series  may 
have  still  another  purpose,  namely,  to  bring  the  total  microphone  re- 
sistance to  its  most  advantageous  value.  In  order  that  the  sounds  are 
reproduced  in  the  receiver  with  maximum  clearness,  the  resistance 
of  the  microphone  or  equivalent  resistance*  of  the  microphone  circuit 
must  have  a  certain  definite  relation  f  to  the  effective  resistance  of  the 
antenna.  This  relation  can  be  obtained,  aside  from  using  several  micro- 
phones, by  the  same  means  as  were  discussed  in  connection  with  the 
similar  problem  in  Art.  178;  that  is,  the  microphone  is  put  in  a  separate 
circuit  whose  coupling  with  the  antenna  can  be  varied  at  will,  or  only  a 
part  of  the  antenna  current  J  is  allowed  to  pass  through  the  microphone, 

*  The  equivalent  resistance  R  of  the  microphone  circuit  is  denned  as  the  value  of 
R  in  RI2eff,  when  this  expression  is  equal  to  the  energy  delivered  to  the  microphone 
circuit  per  second,  /  being  the  current  at  the  base  of  the  antenna. 

f  The  change  produced  in  the  antenna  current  amplitude  by  a  given  change  in  the 
microphone  resistance  is  greatest,  in  the  arrangement  of  Fig.  451,  if  the  microphone 
resistance  is  equal  to  that  of  the  rest  of  the  antenna.329 

$  Or,  to  make  this  more  general,  part  of  the  current  of  that  system  which  is  to  be 
affected  by  the  changes  in  the  microphone. 


WIRELESS  TELEPHONY 


373 


the  latter  being  connected  in  parallel  to  a  portion  of  the  antenna  induct- 
ance or  to  a  condenser  placed  in  the  antenna. 

b.  Instead  of  varying  the  amplitude  of  the  radiated  waves  by  means 
of  a  microphone,  attempts  have  been  made  to  change  the  frequency  of 
the  waves  by  the  microphone  variations;  the  author,  however,  is  not 
aware  of  any  practical  success  in  this  direction. 


FIG.  452. 

210.  Microphones. — Whenever  great  ranges  are  required,  so  that  a 
large  amount  of  energy  must  be  handled  in  the  transmitter,  it  is  in 
general  impossible  to  avoid  sending  heavy  currents  through  the  micro- 
phone. This  at  once  eliminates  the  ordinary  microphones  built  for 
small  currents.  A  great  number  of  contrivances  have  been  devised  to 
meet  this  problem. 

a.  It  has  been  proposed  to  constantly  shake  the  microphones  during 
operation,  to  prevent  excessive  local  heating  of  the  carbon  particles. 
The  same  purpose  is  served  by  devices  in  which  the  microphone  particles 
are  set  into  very  active  motion  by  the  sound  waves.  Then  various 
air,  oil  and  water-cooled  microphones  as,  e.g.,  the  heavy  current  micro- 
phone of  C.  EGNER  and  J.  G.  HoLMSTROM330  have  been  devised. 

6.  The  hydraulic  microphone  of  S.  MAJORANA331  seems  to  have  given 
particularly  good  results  (Fig.  453). 

A  liquid  flows  from  a  tube  Ri,  which  has  an  elastic  diaphragm  at  A 


374 


WIRELESS  TELEGRAPHY 


re- 


to the  diaphragm  M  of  the  microphone,  and  impinges  upon  a 
plate  P  where  it  forms  a  thin  liquid  sheet  or  layer.  This  layer  acts  as  a 
conductor  between  the  metallic  (platinum)  plate  PI  and  the  metallic 
ring  P2  (Po  is  made  of  insulating  material).  As  long  as  the  diaphragm 
remains  at  rest  the  liquid  flows  in  a  fine  even  stream.  But  if  the  dia- 
phragm is  vibrated,  the  stream  assumes  contractions  in  unison  with 
the  vibrations,  and  the  resistance  of  the  sheet  of  liquid  joining  the  two 

platinum  electrodes  PI  and  P%  also  varies  in 
unison  with  the  vibrations. 

With  this  microphone,  in  conjunction  with 
a  POULSEN  500  volt  generator,  successful  tests 
were  conducted  between  two  fixed  stations  of 
moderate  size  about  500  km.  apart  and  be- 
tween a  fixed  station  and  a  torpedo  boat  de- 
stroyer station  over  400  km.  apart. 

c.  Another  hydraulic  microphone  (Fig.  454) 
was  devised  by  F.  J.  CHAMBERS.332  Here  the 
vibrations  of  diaphragm  M  vary  the  resistance 
of  the  very  thin  layer  of  liquid  between  M  and 
the  fixed  tubular  electrode  E,  which  also  serves 

M 


PtP0Pa 

FIG.  453. 


FIG.  454. 


for  feeding  the  liquid.     This  microphone  is  claimed  to  stand  from  250  to 
500  watts  and  to  give  very  clear  reproductions. 

d.  R.  A.  FESSENDEN325  has  constructed  a  telephone  relay  which  is 
claimed  to  allow  the  use  of  a  current  of  15  amp. 

2.  THE  RECEIVER 

211.  Connections. — a.  In  general  the  receivers  used  for  radio-tele- 
phony must  meet  the  same  general  requirements  as  radio-telegraph 
receivers.  The  methods  of  connection  consequently  have  little  if  any 
difference. 

Formerly  it  was  considered  "important  to  have  very  sharp  tuning  in 
the  receiver,  so  that  the  resonance  circuits  in  the  receiver  were  designed 
with  as  little  damping  as  possible. 

Thus,  the  PouLSEN328  method,  shown  in  Fig.  455,  is  an  example  of 


WIRELESS  TELEPHONY 


375 


this  class.  Here  the  aerial  is  coupled  with  a  condenser  circuit  CiSi  and 
this  in  turn  with  the  condenser  circuit  C2£2.  In  the  latter  the  damping 
is  intentionally  kept  low  by  connecting  the  detector  Th  in  parallel 
with  only  a  portion  of  the  self-induction  $2.  The  commercial  con- 
struction of  this  arrangement  is  shown  in  Fig.  452  (left-hand  side);  the 
adjustable  condenser  at  the  extreme  left  is  C% 
of  Fig.  455,  while  that  furthest  to  the  right 
is  Ci  and  consists  of  an  upper  part  adjustable 
in  steps  and  a  lower  part  continuously  ad- 
justable. Between  these  condensers  are  the 
coupling  coils  SiSz  which  are  arranged  for 
adjustable  coupling  as  shown  in  Fig.  382. 

Very  soon,  however,  low  damping  in  the 
resonance  circuits  of  the  receiver  was  aban- 
doned. It  developed  that  the  resonance  action 
causes  a  distortion  of  the  speech  transmitted. 
This,  in  fact,  is  to  be  expected  if  we  consider 
the  relations  discussed  in  Art.  67.  The  time 
variation  of  the  amplitude  in  the  resonant  system  in  general  follows 
the  time  variation  of  the  amplitude  in  the  exciting  system  more  closely 
the  higher  the  damping  of  the  resonant  system  is,  i.e.,  the  more  the 
impressed  oscillations  preponderate  over  the  natural  oscillations.  Ac- 
cordingly, for  clear  reproduction  of  speech  it  is  better  that  the  damping  of 
the  receiving  antenna  is  not  too  low  and  that  a  closed  (aperiodic)  or,  at  any 
rate,  highly  damped  detector  circuit  is  coupled  to  the  antenna. 


FIG.  456. 


FIG.  457. 


This  idea  was  carried  out  in  the  arrangement  (Fig.  456*)  formerly  used 
by  the  TELEFTJNKEN  Co.  and  also  in  that  apparently  now  in  use  by 
PouLSEN328  (Fig.  457).  In  the  latter,  however,  an  additional  resonance 
circuit  containing  condenser  C2  is  used,  but  this  circuit  must  be  very 
highly  damped  as  detector  Th  is  connected  directly  in  circuit. 

*  C"  is  a  block  condenser. 


376 


WIRELESS  TELEGRAPHY 


b.  In  those  methods  in  which  the  frequency  instead  of  the  amplitude 
of  the  transmitter  oscillations  is  varied  by  the  microphone,  it  is  important 
that  the  receiver  is  not  tuned  exactly  to  the  transmitter  frequency.334 
Otherwise,  in  view  of  the  relatively  flat  peak  of  the  resonance  curve,  the 
amplitude  in  the  receiver  would  be  only  slightly  changed  (A)  by  a  given 
change  (dNt  Fig.  458)  in  the  frequency.  But  if  the  receiver  is  not  quite 

in  tune  with  the  transmitter,  so 
that  we  are  working  on  the  rising  or 
falling  side  of  the  resonance  curve 
instead  of  at  the  peak,  the  same 
change,  dN,  in  frequency  causes  a 
considerably  greater  change,  B,  in 
the  amplitude.* 

c.  The  calling  of  a  desired  radio- 
telephone station  would  also  be 
made  possible  by  the  method  de- 
scribed in  Art.  1696.  Another 
method  which  has  been  proposed,335 
is  to  so  adjust  the  receiving  station 
FIG.  458.  for  being  called  that  the  coupling 

between    receiving    antenna    and 

detector  circuit  is  as  close  as  possible  and  the  normal  telephone  used  for 
talking  is  replaced  by  a  loud-speaking  telephone. 

212.  The  Action  in  the  Detector  Circuit. — a.  If  a  pure  note  or  tone  is 
sung  or  played  into  the  transmitting  microphone,  the  amplitude  of  the 
wave  which  is  radiated  oscillates  in  the  period  of  this  note.  The  ampli- 
tude in  the  detector  circuit  must  oscillate  at  the  same  frequency,  so  that 
its  curve  would  be  of  the 
form  of  Fig.  459a.  There- 
fore, in  the  detector  (which 
we  may  assume  to  be  a 
thermal  detector)  there 
would  be  a  corresponding 
e.m.f.  with  time  variation 
as  represented  by  Fig.  4596. 
It  follows  that  the  current 
obtained  in  the  receiving 
telephone  has  the  same 
periodicity  as  the  rise  and  fall  of  the  amplitude  of  the  transmitter  oscil- 
lations and  therefore  is  of  the  same  period  as  the  tone  impressed  upon  the 
microphone  in  the  transmitter. 

6.  Similarly,  if  a  sound  other  than  a  pure  note,  and  consisting  of  a 

*  The  same  relation  holds  for  wireless  telegraphy  in  cases  where  the  signals  are 
produced  by  varying  the  frequency  [Art.  127c]. 


FIG.  459. 


WIRELESS  TELEPHONY  377 

fundamental  and  a  large  number  of  upper  harmonics,  is  spoken  into  the 
microphone  the  same  relation  holds. 

If,  in  this  case,  the  telephone  current  is  to  accurately  reproduce  the 
amplitude  fluctuations  of  the  transmitter  waves,*  then,  aside  from  the 
requirement  discussed  in  Art.  21  la,  the  detector  must  quantitatively 
follow  the  rapid  amplitude  fluctuations,  i.e.,  must  develop  direct-current 
energy  approximately  in  proportion  to  the  high  frequency  energy  sup- 
plied to  it.  Hence  thermal  or  crystal  detectors |  which  fill  this  require- 
ment are  mostly  used. 


THE  DEVELOPMENT  OF  WIRELESS  TELEGRAPHY  DURING  THE  YEARS 

1909  TO   1912 

a.  Probably  the  most  prominent  feature  in  the  development  of  wire- 
less telegraphy  during  the  last  few  years  has  been  the  general  adoption 
of  a  musical  tone  in  the  receiving  telephone. 

Of  the  advantages  thereby  attainable,  viz., 

1.  Oral  reception  is  made  easier  and  more  sensitive, 

2.  Greater  freedom  from  atmospheric  disturbances  [Art.  1836], 

3.  The  principle  of  acoustic  resonance  can  be  made  use  of  [Arts.  1666, 
167d,  1696], 

4.  Duplex  reception  with  the  same  electric  wave-length,336  the  first 
two  have  certainly  proven  themselves  to  be  very  valuable.     This  ac- 
counts for  the  many  different  methods  which  have  been  devised  for 
producing  a  tone  in  the  telephorie  receiver. 

A.  The  most  obvious  thing  to  do,  which  A.  BLONDEL  had  suggested 
as  early  as  1900,  was  to  give  to  the  frequency  of  the  desired  tone  to  the 
wave  at  its  point  of  origin,  the  transmitter — "tone  transmitter." 

A  great  number  of  methods  for  accomplishing  this  with  damped  waves 
have  been  proposed,  thus: 

1.  For  A.C.  operation,  the  use  of  an  A.C.  generator  of  sufficiently  high 
frequency  [Art.  1 14]  either  alone  or  combined  with  a  rotating  spark  gap 
[Art.  118]. 

2.  For  D.C.  operation,  control  of  the  discharge  frequency  by  means  of 
a  rotating  spark  gap  with  projecting  electrodes  [Art.  1186],  or 

3.  Superimposing  an  alternating  current  obtained  from  an  arc  circuit 
upon  a  constant  direct  current,  an  arrangement  which  offers  a  par- 
ticularly easy  means  of  varying  the  tone  [Art.  128]. 

4.  The  same  advantage  is  secured  by  a  new  method  devised  by  A. 

*  It  is  assumed  that  the  amplitude  fluctuations  of  the  transmitter  waves  accurately 
reproduce  the  fluctuations  impressed  upon  the  microphone. 

t  MAJORANA331  obtained  good  results  with  an  iron  pyrites — platinum  detector 
and  particularly  with  DE  FOREST'S  "auction,"  in  the  form  shown  in  Fig.  342  having 
three  electrodes. 


378  WIRELESS  TELEGRAPHY 

MEISSNER  (TELEFUNKEN  Co.);  in  this  a  periodic  auxiliary  discharge 
causes  the  main  discharge  to  occur  periodically  with  the  same  frequency 
as  the  auxiliary  discharge.337 

Similarly  a  great  number  of  methods  for  producing  a  tone  transmitter 
have  been  devised  for  undamped  oscillations. 

1.  It  was  proposed  to  break  up  the  continuous  oscillations  of  the 
antenna  into  a  sequence  of  regular  wave  trains  by  means  of  an  inter- 
rupter.338 

2.  To  vary  the  amplitude  of  the  radiated  wave  at  the  frequency  of  the 
desired  tone  by  means  of  an  arc  circuit  acting  upon  the  high  frequency 
generator.339 

3.  To  produce  fluctuations  in  the  antenna,  either  by  causing  two  arc 
generators  slightly  out  of  tune  to  act  upon  the  antenna  (C.  LoRENZ340) 
or,  if  a  high  frequency  alternator  is  used,  by  means  of  special  connections 
of  the  groups  of  coils  in  the  windings  of  the  machine  (R.  GoLDSCHMiDT341). 

B.  But  with  undamped  oscillations  it  is  undoubtedly  simpler  to 
leave  the  amplitude  of  the  radiated  waves  constant  and  to  make  pro- 
vision for  "tone  reception"  at  the  receiving  end. 

1.  The  first  means  which  offers  itself  for  this  purpose  is  to  periodically 
connect  and  disconnect  the  detector  from  the  receiving  circuits  [Art.  187]. 

2.  Then,  it  is  also  possible  to  obtain  tone  reception  by  combining 
with  the  oscillation  induced  in  the  receiver  by  the  transmitted  waves, 
another  oscillation  of  somewhat  different  frequency  [Art.  190]. 

Some  of  the  methods  mentioned  above  have  probably  never  found 
practical  application.  If  very  fully  listed  here,  it  was  with  the  idea  of 
illustrating  the  great  number  of  possible  solutions  for  a  given  problem  in 
this  field  of  work — " solutions"  at  any  rate  in  the  patent  papers. 

6.  With  stations  employing  damped  oscillations,  whether  the  WIEN 
or  the  BRAUN  type  of  transmitter  is  used,  the  essential  requirement  for 
tone  transmission  is  a  discharge  frequency  at  least  as  high  as  the  frequency 
of  the  desired  tone,  much  higher  therefore  than  was  formerly  customary. 
At  the  same  energy  and  the  same  decrement  such  a  transmitter  has  a 
much  lower  oscillation  amplitude  than  the  older  transmitter  of  lower 
spark  frequency,  and  therefore  has  a  number  of  technical  advantages  over 
the  latter  [Art.  1206  and  c]. 

The  good  results  obtained  by  raising  the  discharge  frequency  up  to 
that  of  audible  tones,  suggested  raising  the  frequency  still  higher  and  thus 
increasing  the  energy.  When  this  was  attempted,  however,  a  limit  to  the 
frequency  was  very  soon  encountered.  For,  on  one  hand,  the  intensity 
of  the  tone  in  the  receiving  telephone  soon  fails  to  keep  pace  with  the 
energy  when  the  latter  is  increased  in  this  way  and,  on  the  other  hand, 
with  the  long  waves  used  by  high-power  stations,  the  intervals  between 
the  individual  wave  trains  disappear  and  the  wave  trains  overlap  and 
interfere  with  one  another.  Hence  we  have  here  again  reached  the  point 


WIRELESS  TELEPHONY  379 

where  increasing  the  amplitude  is  the  only  path  open  to  us,  if  damped 
oscillations  are  to  be  retained. 

c.  The  alternative  is  to  turn  to  undamped  oscillations.  And  the  fact 
is  that  undamped  oscillations,  particularly  those  produced  by  high  fre- 
quency alternators,  are  coming  to  be  very  serious  competitors  in  the  field 
in  which,  until  recent  years,  there  were  only  three  great  rivals  (the  BRAUN, 
WIEN  and  POULSEN  transmitters). 

The  adoption  of  high  frequency  machines  has  long  been  hampered  by 
the  technical  difficulties  to  be  overcome  in  building  alternators  of  fre- 
quencies sufficiently  high  for  the  requirements  of  radio-telegraphy.  It  is 
comparatively  simple  to  obtain  frequencies  ranging  just  below  those 
needed.  Hence  the  idea  underlying  recent  developments  in  this  direction 
has  been  transformation  of  the  frequency.  Only  a  moderately  high  alter- 
nator frequency,  as  determined  by  the  number  of  poles  and  speed  of  the 
machine,  is  employed,  but  is  then  transformed  to  frequencies  two,  three 
or  more  times  that  of  the  original  value. 

R.  GOLDSCHMIDT  may  be  named  as  the  first  one  to  introduce  this  idea 
in  radio-practice,  if  we  conceive  his  method  [Art.  122]  as  a  frequency 
transformation  within  the  alternator. 

As  early  as  1898,  a  method  of  transforming  the  frequency  of  an 
alternating  current  outside  of  the  machine  to  twice  the  original  frequency 
by  means  of  rectifying  cells  was  pro-  __^__ 

posed  (J.  ZENNECK342). 


If   an   alternating  current  of  the    J,  o 
form  of  Fig.  460a  is  sent  through  a    |  — *Time 
rectifying   cell  or  tube,  which  allows   o 
current    to    pass   through   it  in  one 
direction  only,  the  resultant  current 
curve  will  be  as  shown  in  Fig.  4606. 
If  the  connections  of  the  rectifier  are 
reversed,   the  current  curve   will   be 
as  shown  in  Fig.  460c.     If  the  two 
resultant  currents  (Fig.  4606  and  c) 

obtained  in  this  manner  are  caused  to  act  inductively  upon  a  third 
circuit — preferably  a  condenser  circuit  tuned  to  twice  the  original 
frequency— a  current  of  the  form  of  Fig.  460d,  having  double  the  initial 
frequency,  will  be  obtained  in  the  third  circuit.  The  e.m.f.  induced  in 
this  resonant  condenser  circuit  has  of  course  double  the  frequency  of 
the  initial  e.m.f.  also. 

Another  method  for  doubling  the  frequency  was  first  described  by 
the  LAHMEYER  Co.  (EPSTEIN343)  and  has  been  adapted  for  high  frequency 
work  by  COUNT  v.  ARCO  (TELEFUNKEN  Co.344).  This  method  is  based 
upon  the  magnetic  properties  of  iron. 

The  principle  involved  is  as  follows:    Through  one  of  two  windings 


380 


WIRELESS  TELEGRAPHY 


on  an  iron  transformer  core,  direct  current  is  passed  of  such  magnitude 
that  the  flux  density  in  the  iron — represented  in  Fig.  4616  and  c  by 
the  dotted  lines — is  just  about  at  the  knee  of  the  magnetization  curve. 
Then,  if  alternating  current  is  sent  through  the  other  winding,  it  can 
produce  only  a  slight  increase  in  the  flux  density  during  the  half  periods 
in  which  its  field  has  the  same  direction  as  the  direct-current  field;  but 
in  the  other  half  periods  when  the  alternating  current  is  reversed,  it 

will   greatly   reduce   the  resultant 
flux  density.     The  curve  of  the  re- 
a    sultant  magnetic  flux  must,  there- 
fore, have  the  form  of  Fig.  4616. 
By   commutating    the    alternating 
b    current  a  flux  curve  of  the  form  of 
Fig.  461c  is  obtained.     If,  now,  two 
varying  fluxes  of  the  forms  of  Fig. 
c    4616  and  c  respectively  are  simul- 
taneously caused  to  act  inductively 
upon  a  conductive  circuit — as  be- 
fore, preferably  a  condenser  circuit 
tuned   to   the  double  frequency— 
the  total  resultant  flux  acting  upon 
•plG  461  this  circuit  will  be  the   algebraic 

sum  of  the  two  individual  fluxes 

and  will  have  the  form  of  Fig.  461d  This  will,  therefore,  induce  an 
e.m.f.  of  twice  the  original  frequency  in  the  condenser  circuit. 

A  third  method  (J.  ZENNECK345),  by  means  of  which  the  original  fre- 
quency can  be  tripled,  makes  use  of  the  strong  third  harmonic  (second 
upper  partial  oscillation)  which  is  characteristic  of  the  potential  across 
an  alternating-current  arc. 

If  a  self-induction  and  capacity  are  connected  across  the  poles  of 
an  A.C.  arc,  similarly  to  the  THOMSON  or  POULSEN  methods  [Art.  123], 
a  heavy  current  of  three  times  the  frequency  of  the1  supply  current  will 
be  obtained  in  this  parallel  condenser  circuit,  if  the  capacity  and  self- 
induction  values  are  properly  chosen. 

Of  these  three  methods,  only  the  second,  as  developed  by  COUNT 
V.  ARCO  (TELEFUNKEN  Co.) ,  appears  to  have  been  commercially  applied  to 
high  frequency  work.  But  even  in  regard  to  this  method  very  little 
has  been  published  as  to  the  actual  results  obtained,  other  than  that 
with  an  initial  frequency  of  7500  cycles  per  second  (X  =  40,000  m.) 
the  efficiency  of  one  transformation  is  about  85  per  cent,  and  that  of 
two  transformations  (four  times  the  initial  frequency)  is  still  60  per 
cent.344 

A  conclusive  opinion  as  to  the  value  of  these  methods  will  not  be 
possible  until  additional  performance  data  are  available  and,  more 


WIRELESS  TELEPHONY  381 

particularly,  until  we  know  to  what  extent  the  difficult  problem  of  hold- 
ing the  speed  of  a  high  frequency  alternator  constant,  has  been  solved. 

d.  If  the  use  of  high  frequency  alternators  in  conjunction  with  one  of 
these  frequency  transformation  methods  should  prove  to  be  a  practical 
success,  then  this  would  at  the  same  time  be  a  great  step  forward  for 
directive   signaling,  which   has  greatly  increased  in  importance  during 
the  last  few  years.     For  with  alternators  it  is  much  easier  to  produce 
a  given  phase  difference  between  two  high  frequency  currents — for  in- 
stance by  coupling  two  machines  to  each  other  or  by  having  two  armatures 
slightly  displaced  with  respect  to  each  other  in  the  same  machine — than 
with  the  earlier  methods  [Arts.  200  and  201]  which  moreover  never  seem 
to  have  found  any  practical  application.     But  as  soon  as  it  becomes  a 
relatively  simple  matter  to  generate  high  frequency  currents  having  any 
desired  phase  difference,  a  means  of  building  directive  transmitters  hav- 
ing much  more  advantageous  distance  effect  characteristics  than  here- 
tofore will  be  at  hand. 

e.  Then,  too,  it  will  perhaps  be  more  convenient  to  generate  the  large 
quantities  of  energy  needed  in  modern  high-power  stations  in  alternators 
than  with  the  older  methods. 

The  energy  quantities  employed  in  radio-telegraphy  have  been  greatly 
increased  during  recent  years.  Whereas  only  a  few  years  ago,  stations 
operating  with  100  kw.  were  considered  as  something  tremendous,  it  is 
reported  that  the  MARCONI  transatlantic  stations  are  being  equipped 
with  1100  hp.,  and  the  TELEFTJNKEN  Co.  is  building  a  500  kva.  high  fre- 
quency alternator.  If  we  compare  these  high  powers  with  the  ex- 
tremely low  amounts  of  energy  supplied  in  the  early  days  of  wireless 
telegraphy  from  small  storage  batteries  to  operate  an  induction  coil  and 
then  compare  the  ranges  obtained  at  that  time  with  those  now  attain- 
able, it  would  seem,  at  first  glance,  as  if  the  actual  results  obtained  have 
not  kept  pace  with  the  increased  energy  employed  in  spite  of  the  many 
technical  improvements  in  the  art.  There  may,  in  fact,  be  some  truth 
in  this  (see  g),  but  the  explanation  lies  partly  in  the  fact  that  we  now  are 
more  critical  of  range  ratings  than  formerly  and  that  our  conception  of 
range  alway  includes  the  idea  of  constant  reliable  operation.  Then,  too, 
it  has  been  found  that  the  decrease  in  amplitude  of  an  advancing  wave 
is  more  rapid  even  over  sea  water  [Art.  1466]  than  was  formerly  believed 
to  be  the  case,  so  that  an  increase  in  range  necessitates  a  much  greater 
increase  in  radiated  energy  than  was  expected. 

/.  The  same  tendency  toward  larger  dimensions  in  the  recent  de- 
velopment of  radio-telegraphic  methods  which  manifested  itself  in  in- 
creased energy  also  has  led  to  increased  wave-lengths.  For  high-power 
stations  we  have  gradually  reached  7000  m.  waves,  primarily,  no  doubt, 
because  of  the  better  daylight  distance  effect  of  the  longer  waves  as 
compared  to  the  shorter  and,  secondly,  as  the  use  of  larger  amounts  of 


382  WIRELESS  TELEGRAPHY 

energy,  at  any  rate  in  the  primary  circuits  of  the  transmitters  is  simpler 
with  long  than  with  short  waves. 

g.  The  effect  of  this  general  tendency  upon  the  antenna  has  like- 
wise been  a  transition  to  ever-increasing  dimensions  [Art.  92c,  202]. 
When  practical  structural  limits  were  reached,  refuge  was  taken  in  coils 
inserted  in  the  antenna  to  increase  its  self-induction  or  in  the  "  fly- 
wheel" method  of  connection.  This,  however,  greatly  reduced  the  radia- 
tion resistance.  While  this  is  very  advantageous  for  reception  both 
in  regard  to  effectiveness  of  the  receiver  [Art.  172]  as  well  as  in  regard 
to  the  simplicity  of  the  connections  [Art.  176],  it  is  correspondingly  dis- 
advantageous for  the  transmitter  [Art.  99].  The  efficiency  is  greatly 
reduced,  only  a  very  small  part  of  the  energy  being  radiated,  in  spite  of 
all  known  methods  for  minimizing  the  antenna  losses.  Marconi  seems 
to  have  drawn  the  right  conclusions  from  these  relations  in  that  he  has 
separated  the  transmitting  and  receiving  antennae  in  his  transatlantic 
stations,  using  an  antenna  of  low  radiating  power  for  reception  and  one 
of  greater  radiating  power  for  transmission. 

But  the  chief  difficulty  is  encountered  in  the  "  antenna  with  high  radia- 
tion resistance."  Just  how  great  this  is  in  the  bent  MARCONI  antenna, 
has  not  become  known.  In  vertical  antennae,  an  increase  in  the  radia- 
tion resistance  is  identical  with  an  increase  in  the  height  of  the  antenna, 
the  wave-length  remaining  the  same;  this  correct  but  by  no  means  simple 
method  has  been  introduced  by  the  TELEFUNKEN  Co.  in  its  great  antenna 
(200  m.  high)  at  Nauen. 

h.  The  development  of  radio-telegraphy  as  a  whole  in  recent  years 
can  undoubtedly  be  considered  as  very  gratifying.346  The  great  import- 
ance of  wireless  telegraphy  as  a  factor  in  the  safety  of  ships  and  their 
passengers,  has  resulted  in  laws  and  regulations  obligating  the  installa- 
tion of  radio-equipment  on  all  ships  above  a  certain  size. 

Furthermore,  the  field  of  application  of  wireless  telegraphy  has  ex- 
tended considerably.  Whereas  it  formerly  was  used  only  for  the  trans- 
mission of  ordinary  telegrams,  it  now  serves  as  a  means  for  furnishing 
ships  at  sea  with  regular  standard  time  signals347  and  storm  warnings,348 
for  the  determination  of  geographic  longitudes349  and  also  for  the  remote 
control  of  experimental  recording  balloons  and  similar  meteorological 
purposes.350-*  Thus  radio-telegraphy  has  already  found  a  much  more 
extensive  application  than  one  dared  to  hope  for  in  the  early  years  of  its 
use. 

*  [Translator's  Note. — Recent  developments  in  connection  with  wireless  signaling 
for  railroad  operation  seem  to  indicate  the  opening  of  still  another  field.] 


TABLES 


383 


384 


WIRELESS  TELEGRAPHY 


Table  I.— The  Natural 


=  •=  number  of  complete  periods  or  cycles  per  second  [Art.  3]. 


N    =   ; 

In  the  following  table  the  capacity  is  expressed  in  1/1000  mf.  =  10~18  c.g.s. 
units  and  the  coefficient  of  self-induction  in  c.g.s.  units.  The  figures  given  must  be 
multiplied  by  106  to  give  the  values  of  N. 

The  following  examples  illustrate  how  the  table  is  used  for  values  of  C  and  L  other 
than  those  given: 


i 

1.1 

1.2 

1.3 

1.4 

1.5 

2 

2.5 

3 

100 

15.9 

15.2 

14.5 

14.0 

13.4 

13.0 

11.3 

10.1 

9.19 

110 

15.2 

14.5 

13.9 

13.3 

12.4 

12  .4 

10.7 

9.60 

8.76 

120 

14.5 

13.9 

13.3 

12.7 

12.3 

11.9 

10.3 

9.19 

8.39 

130 

14.0 

13.3 

12.7 

12.2 

11.8 

11.4 

9.87 

8.83 

8.64 

140 

13.4 

12.8 

12.3 

11.8 

11.4 

11.0 

9.51 

8.51 

7.77 

150 

13.0 

12.4 

11.9 

11.4 

11.0 

10.6 

9.19 

8.22 

7.50 

200 

11.3 

10.7 

10.3 

9.87 

9.51 

9.19 

7.96 

7.12 

6.50 

250 

10.1 

9.60 

9.19 

8.83 

8.51 

8.22 

7.12 

6.37 

5.81 

310 

9.19 

8.76 

8.39 

8.64 

7.77 

7.50 

6.50 

5.81 

5.305 

£     350 

8.51 

8.11 

7.77 

7.46 

7.19 

6.95 

6.01s 

5.38 

4.91 

g     400 

7.96 

7.59 

7.26 

6.98 

6.72 

6.50 

5.63 

5.03 

4.59 

.     450 

7.50 

7.15 

6.85 

6.58 

6.34- 

6.13 

5.30s 

4.74s 

4.33 

3)    500 

7.12 

6.79 

6.50 

6.24 

6.01s 

5.81 

5.03 

4.50 

4.11 

.3     60° 

6.50 

6.20 

5.93 

5.70 

5.49 

5.305 

4.59 

4.11 

3.75 

6.02 

5.74 

5.49 

5.28 

5.08 

4.91 

4.25 

3.80s 

3.47 

§     800 

5.63 

5.37 

5.14 

4.93s 

4.76 

4.59 

3.98 

3.56 

3.25 

'•g     900 

5.31 

5.06 

4.84 

4.65 

4.48 

4.33 

3.75 

3.355 

3.06 

la   1000 

5.03 

4.80 

4.59 

4.41 

4.25 

4.11 

3.56 

3.18 

2.91 

3   1100 

4.80 

4.56 

4.38 

4.21 

4.06 

3.92 

3.39 

3.03s 

2.77 

H   1200 

4.59 

4.38 

4.19 

4.03 

3.88 

3.75 

3.25 

2.91 

2.65 

«*-   1300 

4.41 

4.21 

4.03 

3.87 

3.73 

3.60 

3.12 

2.79 

2.55 

°.   1400 

4.25 

4.06 

3.88 

3.73 

3.60 

3.47 

3.01 

2.69 

2.46 

ttt 

o   1500 

4.11 

3.92 

3.75 

3.60 

3.47 

3.355 

2.91 

2.60 

2.37 

^  2000 

3.56 

3.39 

3.25 

3.12 

3.01 

2.91 

2.52 

2.25 

2.055 

2500 

3.18 

3.03s 

2.91 

2.79 

2.69 

2.60 

2.25 

2.01 

1.84 

3000 

2.91 

2.77 

2.65 

2.55 

2.46 

2.37 

2.05s 

1.84 

1.68 

3500 

2.69 

2.56s 

2.46 

2.36 

2.27 

2.20 

1.90 

1.70 

1.55 

4000 

2.52 

2.40 

2.30 

2.21 

2.13 

2.055 

1.78 

1.59 

1.45 

4500 

2.37 

2.26 

2.17 

2.08 

2.005 

1.94 

1.68 

1.50 

1.37 

5000 

2.25 

2.15 

2.05 

1.97 

1.90 

1.84 

1.59 

1.42 

1.30 

6000 

2.05 

1.96 

1.88 

1.80 

1.74 

1.68 

1.45 

1.30 

1.19 

7000 

1.90 

1.81 

1.74 

1.67 

1.61 

1.55 

1.34 

1.20 

1.10 

8000 

1.78 

1.70 

1.61 

1.56 

1.50 

1.45 

1.26 

1  .  125 

1.03 

9000 

1.68 

1.60 

1.53 

1.47 

1.42 

1.37 

1.19 

1.06 

0.969 

TABLES 


385 


Frequency  of  Condenser  Circuits351 

1.  C  =  11  X  10-3mf.;  L  =  800  c.g.s. 

.-.if- 


27rV800  X  (11  X  10~18)       27TV8000  X  1.1  X  10~18 
=  1.70  X  106  cycles  per  second. 
2.  C  =  0.45  mf.;L  =  7000  c.g.s. 


27TV7000  X  (450 X10-18)       2w  X  10  V7000  X  4.5  X  10~18 
=  0.897  X  105  cycles  per  second. 


3.5 

4 

4.5 

5 

6 

7 

8 

9  X  10 

-3mf. 

8.51 

7.96 

7.50 

7.12 

6.50 

6.02 

5.63 

5.31 

8.11 

7.59 

7.15 

6.79 

6.20 

5.74 

5.37 

5.06 

7.77 

7.26 

6.85 

6.50 

5.93 

5.49 

5.14 

4.84 

7.46 

6.98 

6.58 

6.24 

5.70 

5.28 

4.93s 

4.65 

7.19 

6.72 

6.34 

6.01s 

5.49 

5.08 

4.76 

4.48 

6.95 

6.50 

6.13 

5.81 

5.30s 

4.91 

4.59 

4.33 

6.01s 

5.63 

5.30s 

5.03 

4.59 

4.25 

3.98 

3.75 

5.38 

5.03 

4.74s 

4.50 

4.11 

3.80s 

3.56 

3.35s 

4.91 

4.59 

4.33 

4.11 

3.75 

3.47 

3.25 

3.06 

g    4.55 

4.25 

4.01 

3.80s 

3.47 

3.21s 

3.01 

2.84 

'3    4.25 

3.98 

3.75 

3.56 

3.25 

3.01 

2.81 

2.65 

.    4.01 

3.75 

3.54 

3.35s 

3.06 

2.84 

2.65 

2.50 

So   3'8°5 

3.56 

3.35s 

3.18 

2.91 

2.69 

2.52 

2.37 

o 

rt    3.47 

3.25 

3.06 

2.91 

2.65 

2.46 

2.30 

2.17 

'3    3.21s 

3.01 

2.84 

2.69 

2.46 

2.27 

2.13 

2.00s 

o    3.01 

2.81 

2.65 

2.52 

2.30 

2.13 

1.99 

1.88 

'•£    2.84 

2.65 

2.50 

2.37 

2.17 

2.00s 

1.88 

1.77 

13    2.69 

2.52 

2.37 

2.25 

2.05 

1.90 

1.78 

1.68 

J,    2.56s 

2.40 

2.26 

2.15 

1.96 

1.81 

1.70 

1.60 

g    2.46 

2.30 

2.17 

2.05 

1.88 

1.74 

1.62 

1.53 

««    2.36 

2.21 

2.08 

1.97 

1.80 

1.67 

1.56 

1.47 

d    2'27 

2.13 

2.00s 

1.90 

1.74 

1.61 

1.50 

1.42 

r°    2.20 

2.05s 

1.94 

1.84 

1.68 

1.55 

1.45 

1.37 

w       .90 

1.78 

1.68 

1.59 

1.45 

1.34s 

1.26 

1.19 

.70 

1.59 

1.50 

1.42 

1.30 

1.20 

1.12s 

1.06 

.55 

1.45 

1.37 

1.30 

1.19 

1.10 

1.03 

0.969 

.44 

1.34s 

1.27 

1.20 

1.10 

1.02 

0.951 

0.897 

.345 

1.26 

1.19 

1.12s 

1.03 

0.951 

0.890 

0.839 

.27 

1.19 

1.12 

1.06 

0.969 

0.897 

0.839 

0.791 

.20 

1.12s 

1.06 

1.01 

0.919 

0.851 

0.796 

0.750 

1.10 

1.03 

0.969 

0.919 

0.839 

0.777 

0.726 

0.685 

1.02 

0.951 

0.897 

0.851 

0.777 

0.719 

0.673 

0.634 

0.951 

0.890 

0.839 

0.796 

0.726 

0.673 

0.629 

0.593 

0.897 

0.839 

0.791 

0.750 

0.685 

0.634 

0.593 

0.572 

25 


386 


WIRELESS  TELEGRAPHY 


Table  II.— The  Natural  Wave- 

X  =  faVCL  X  1010cm.  =  67rVCL  X  10%!.  [See  second  foot-note  to 
Art.  3o], 

In  the  following  table  the  capacity  is  expressed  in  1/1000  mf.  =  10~18  c.g.s.  units 
the  coefficient  of  self-induction  in  c.g.s.  units.  The  figures  in  the  table  give  the 
wave-length  in  meters. 

The  following  examples  illustrate  how  the  table  can  be  used  for  values  of  C  and  L 
not  given: 


1 

1.1 

1.2 

1.3 

1.4 

1.5 

2 

2.5 

3 

100 

18.8 

19.8 

20.6 

21.5 

22.3 

23.1 

26.7 

29.8 

32.6 

110 

19.8 

20.7 

21.7 

22.5 

23.4 

24.2 

28.0 

31.3 

34.2 

120 

20.6 

21.7 

22.6 

23.5 

24.4 

25.3 

29.2 

32.65 

35.8 

130 

21.5 

22.5 

23.5 

24.5 

25.4 

26.3 

30.4 

34.0 

37.2 

140 

22.3 

23.4 

24.4 

25.4 

26.4 

27.3 

31.5 

35.3 

38.6 

150 

23.1 

24.2 

25.3 

26.3 

27.3 

28.3 

32.65 

36.5 

40.0 

200 

26.7 

28.0 

29.2 

30.4 

31.5 

32.65 

37.7 

42.  15 

46.2 

250 

29.8 

31.3 

32.65 

34.0 

35.3 

36.5 

42.  16 

47.1 

51.6 

300 

32.6 

34.2 

35.8 

37.2 

38.6 

40.0 

46.2 

51.6 

56.0 

«5    350 

35.3 

37.0 

38.6 

40.2 

41.7 

43.2 

49.9 

55.8 

61.1 

•"tn      400 

37.7 

39.5 

41.3 

43.0 

44.6 

46.2 

53.3 

59.6 

65.3 

§   450 

40.0 

41.9 

43.8 

45.6 

47.3 

49.0 

56.  55 

64.4 

69.3 

«B   500 

42.1 

44.2 

46.2 

48.1 

49.9 

51.6 

59.6 

66.6 

73.0 

»   600 

46.2 

48.4 

50.6 

52.6 

54.6 

56.  55 

65.3 

73.0 

80.0 

.S   700 

49.9 

52.3 

54.6 

56.9 

59.0 

61.1 

70.5 

78.  85 

86.4 

a   800 

53.3 

55.9 

58.4 

60.8 

63.1 

65.3 

75.4 

84.3 

92.3 

•2   900 

56.5 

59.3 

61.  95 

64.5 

66.9 

69.3 

80.0 

89.4 

97.9 

o 

-d   1000 

59.6 

62.5 

65.3 

68.0 

70.6 

73.0 

84.3 

94.2 

103 

•S   1100 

62.5 

65.6 

68.5 

71.3 

74.0 

76.6 

88.4 

98.8 

108 

Jt5   1200 

65.3 

68.5 

71.5 

74.  45 

77.3 

80.0 

92.3 

103 

113 

8   1300 

68.0 

71.3 

74.  45 

77.5 

80.4 

83.2 

96.1 

107.5 

118 

'o   1400 

70.6 

74.0 

77.3 

80.4 

83.  46 

86.4 

99.7 

111.5 

122 

*§   1500 

73.0 

76.6 

80.0 

83.2 

86.4 

89.4 

103 

115 

126 

0   2000 

84.3 

88.4 

92.3 

96.1 

96.1 

103 

119 

133 

146 

2500 

94.2 

98.8 

103 

107.5 

111.5 

115 

133 

149 

163 

3000 

103 

108 

113 

118 

122 

126 

146 

163 

179 

3500 

112 

117 

122 

127 

132 

137 

158 

176 

193 

4000 

119 

125 

131 

136 

141 

146 

169 

188.5 

206.5 

4500 

126 

133 

138.5 

144 

150 

155 

179 

200 

219 

5000 

133 

140 

146 

152 

158 

163 

188.5 

211 

231 

6000 

146 

153 

160 

166.5 

173 

179 

206.6 

231 

253 

7000 

158 

165 

173 

180 

187 

193 

223 

249 

273 

8000 

169 

177 

185 

192 

199.5 

206.5 

238 

267 

292 

9000 

179 

188 

196 

204 

212 

219 

253 

283 

310 

TABLES 


387 


length  of  Condenser  Circuits351 

1.  C  =  11  X  10~3  mf.;  L  =  800  c.g.s.  units 
.-.\  =  67iV800  X  (11  X  10~18)  X  108 

=  GTT A/8000  X  1 . 1  X  10~18  X  108  =  177m. 

2.  C  =  0.45  mf.;  L  =  7000  c.g.s.  units 


/.X  =  67TA/7000  X  (450  X  10~18)  X  108 

VTOOO  x  4.5  x  io~18  x  io8] 


3345  m. 


3.5 

4 

4.5 

5 

6 

7 

8 

9  X  IO-3  mf  . 

35.3 

37.7 

40.0 

42.1 

46.2 

49.9 

53.3 

56.5 

37.0 

39.5 

41.9 

44.2 

48.4 

52.3 

55.9 

59.3 

38.6 

41.3 

43.8 

46.2 

50.6 

54.6 

58.4 

61.  95 

40.2 

43.0 

45.6 

48.1 

52.6 

56.9 

60.8 

64.5 

41.7 

44.6 

47.3 

49.9 

54.6 

59.0 

63.1 

66.9 

43.2 

46.2 

49.0 

51.6 

56.  55 

61.1 

65.3 

69.3 

49.9 

53.3 

56.  56 

59.6 

65.3 

70.5 

75.4 

80.0 

55.8 

59.6 

64.4 

66.6 

73.0 

78.  85 

84.3 

89.4 

61.1 

65.3 

69.3 

73.0 

80.0 

86.4 

92.3 

97.9 

66.0 

70.5 

74.8 

78.  85 

86.4 

93.3 

99.7 

106 

70.5 

75.4 

80.0 

84.3 

92.3 

99.7 

107 

113 

74.8 

80.0 

84.8 

89.4 

97.9 

106 

113 

120 

78.  85 

84.3 

89.4 

94.  26 

103 

1116 

119 

126 

86.4 

92.3 

97.9 

103 

113 

122 

131 

138,6 

93.3 

99.7 

106 

111.5 

122 

132 

141 

150 

99.7 

107 

113 

119 

131 

141 

151 

160 

106 

113 

120 

126 

138.5 

150 

160 

170 

112 

119 

126 

133 

146 

158 

169 

179 

117 

125 

133 

140 

153 

165 

177 

188 

122 

131 

138.5 

146 

160 

173 

185 

196 

127 

136 

144 

152 

166.5 

180 

192 

204 

132 

141 

150 

158 

173 

187 

199.5 

212 

137 

146 

155 

163 

179 

193 

206.5 

219 

158 

169 

179 

188.5 

206.5 

223 

238 

253 

176 

188.5 

200 

211 

231 

249 

267 

283 

193 

206.5 

219 

231 

253 

273 

292 

310 

209 

223 

237 

249 

273 

295 

315 

334.5 

223 

238 

253 

267 

292 

315 

337 

358 

237 

253 

268 

283 

310 

334.5 

358 

379 

249 

267 

283 

298 

326.5 

353 

377 

400 

273 

292 

310 

326.5 

358 

386 

415 

438 

295 

315 

334.5 

353 

386 

417 

446 

473 

315 

337 

358 

377 

415 

446 

477 

506 

334.5 

358 

379 

400 

438 

473 

506 

536.5 

388 


WIRELESS  TELEGRAPHY 


Table  III. — Frequency  and  Wave-length 

_  3  X  1010  (cm.  per  sec.)  _  3  X  108  (meters  per  sec.) 
=  X  (cm.)  ~  X 


X 
in  m. 

N 

X 
inm. 

N 

X 
inm. 

N 

X 
inm. 

N 

100 

3.00XlOR/sec. 

510 

5.88Xl05/sec. 

910 

3.29Xl05/sec. 

2500 

1.18Xl05/sec. 

110 

2.73 

520 

5.77 

920 

3.26 

2600 

1.15 

120 

2.50 

530 

5.66 

930 

3.23 

2650 

1.13 

130 

2.31 

540 

5.56 

940 

3.19 

2700 

1.11 

140 

2.14 

550 

5.45 

950 

3.16 

2750 

1.09 

150 

2.00 

160 

.88    " 

560 

5.36 

960 

3.13    " 

2800 

1.07 

170 

.76 

570 

5.26    " 

970 

3.09    " 

2850 

1.05    " 

180 

.67 

580 

5.17    " 

980 

3.06 

2900 

1.03    " 

190 

.58 

590 

5.08    " 

990 

3.03 

2950 

1.02    " 

200 

.50 

600 

5.00 

1000 

3.00 

3000 

1.00 

210 

.43 

610 

4.92 

1050 

2.86    " 

3050 

9.84X104/sec. 

220 

.36 

6204.84 

1100 

2.73 

31009.67 

230 

.31 

6304.76 

1150 

2.61 

31509.53 

240 

.25 

640 

4.69 

1200 

2.50 

32009.38 

250 

.20 

650 

4.62 

1250 

2.40 

3250 

9.23    " 

260 

1.15 

660 

4.55 

1300 

2.31 

3300 

9.09    " 

270 

1.11 

6704.47 

1350 

2.22    " 

33508.96    " 

280 

1.07 

680 

4.41    " 

1400 

2.14 

3400 

8.82    " 

290 

1.03 

690 

4.35    " 

1450 

2.07 

3450 

8.69    •" 

300 

1.00 

700 

4.29    " 

1500 

2.00 

3500 

8.57 

310 

9.67Xl05/sec. 

710 

4.23 

1550 

1.94 

3550 

8.45 

320 

9.38 

720 

4.17    " 

1600 

1.88 

3600 

8.33 

330 

9.09 

730 

4.11 

1650 

1.82 

3650 

8.22 

340 

8.82 

740 

4.05    " 

1700 

1.76 

3700 

8.11 

350 

8.57 

750 

4.00' 

1750 

1.71 

3750 

8.00    " 

360 

8.33 

760 

3.95 

1800 

1.67 

3800 

7.89 

370 

8.11 

770 

3.91 

1850 

1.62 

3850 

7.79    " 

380 

7.89 

780 

3.85 

1900 

1.58 

3900 

7.69 

390 

7.69 

790 

3.79 

1950 

1.54 

3950 

7.59 

400 

7.50 

800 

3.75 

2000 

1.50 

4000 

7.50    " 

410 

7.32 

810 

3.71 

2050 

1.46 

4100 

7.32 

420 

7.14 

820 

3.66 

2100 

1.43 

4200 

7.14 

430 

6.98 

830 

3.62 

2150 

1.40 

4300 

6.98 

440 

6.82    " 

840 

3.57    " 

2200 

1.36 

4400 

6.82 

450 

6.67 

850 

3.53 

2250 

1.33 

4500 

6.67 

460 

6.52 

860 

3.49    " 

2300 

1.31    " 

4600 

6.52 

470 

6.38 

870 

3.45 

2350 

1.28 

4700 

6.38 

480 

6.25 

880 

3.41 

2400 

1.25 

4800 

6.25 

490 

6.12 

890 

3.37 

2450 

1.22 

490016.12 

500 

6.00 

900 

3.33 

2500 

1.20 

5000 

6.00 

TABLES 


389 


Table  IV. — Oscillation  Curves  for  Various  Decrements 


FIG.  462. 
d  =  0,  Undamped  oscillations. 


FIG.  463. 
d  =  0.003. 


390 


WIRELESS  TELEGRAPHY 


Table  IV.    (Continued) 


FIG.  464. 
d  =  0.01. 


FIG.  465. 
d  =  0.06. 


TABLES 


391 


Table  IV.    (Continued) 


FIG.  466. 
d  =  0.2. 


FIG.  467. 
d  =  0.5. 


392 


WIRELESS  TELEGRAPHY 


Table  V.  The  Spark  (Arc)  Constants352 

According  to  Arts.  96  and  1296,  the  voltage,  V,  across  the  poles  of  a  spark  gap 
(or  arc)  can  be  expressed  in  terms  of  the  current,  /,  flowing  through  the  gap  as  follows: 


(1) 


The  values  of  the  constants  of  the  spark  gap  or  arc,  a  and  6,  depend  upon  the  dis- 
tance between  the  electrodes,  their  material  and  their  condition  and  the  gas  in  the 
gap. 

The  relation  to  the  gap  length,  /,  is  approximately  of  the  form 


6  =  60  +  biff 

1.  Thus  for  direct-current  arcs  in  air  the  following  figures  have  been  determined: 
Electrodes  of  homogeneous  carbon: 


a  =  38.88  +    2.074/*  volts  1 
6  =  11.66  +  10.54/  watts     / 


AYRTON352 
'  AYB 


Electrodes  of  copper 


a  =  21.38+    3.03/  volts 
6  =  10.69  +  15.24/  watts 


Guns  and  ZBBKIKOFF'M 
U 


2.  For  alternating-current  arcs,  equations  (1)  and  (2)  also  hold  true  approximately 
if  V  and  I  are  taken  to  represent  the  effective  voltage  and  current  values.     From 
observations  made  by  HEUBACH352  with  carbon  electrodes  in  air   (current  4.4  and 
6.5  amperes,  N  =  50  cycles  per  sec.),  the  following  equations  were  obtained: 

a  =       23.4  +  1.21/*  volts 
6  =  -  13.8  +  3.71/  watts 

3.  With  damped  high  frequency  currents  (X  =  2500  m.,   C  =  2  X  10~3,  and  1  X  10~3 
mf  .  and  L  =  714  X  103,  and  1480  X  103  e.g.  s.  units  respectively),  measurements  made 
by  D.  RoscHANSKY2  led  to  the  following  expression  for  the  initial  amplitude,  V/0,  of 
the  spark  voltage: 

F/o  =  a0  + 


the  values  found  for  different  electrodes  being: 

Magnesium         Zinc 


34.0 
7.6 


30.0 
10.4 


Copper 
28.0 
10.9 


Silver 
42.0  volts 
10.  4  volts 


*  /  is  in  millimeters. 
f  /  is  in  millimeters. 


TABLES  393 

Table  VI. — Equations  for  Calculation  of  the  Coefficient  of  Self-induction353 

In  the  following  equations  p  denotes  the  radius  of  the  wire,  r  the  radius  of  a  turn, 
I  the  length  of  the  coil  (including  the  insulation  on  the  end  turns),  n  the  total  number 
of  turns,  »i  the  number  of  turns  per  centimeter  and  g  the  pitch  of  the  winding,  i.e., 
the  distance  between  the  axial  centers  of  two  consecutive  turns.  If  the  lengths  are 
expressed  in  centimeters,  the  equations  give  the  coefficient  of  self-induction  in  c.g.s. 
units. 

1.  Wire  Loop. 

8r 

Ls  =  47rr(loge—  —  1.75)  (KIRCHHOFF) 
p 

L*  =  47rr(loge-  -2) 
p 

2.  Cylindrical  coil  with  a  single  layer  of  only  a  few  turns  (B.  STRASSER353) : 
Ls  =  4irr[n (log.—  -  l.75\  +  n(n  -  1)  Aog.  ~-2\-A 


The  values  of  A  and  B  are  given  in  the  table  which  follows. 

3.  Cylindrical  coil  whose  length  is  great  in  comparison  to  its  diameter.     For 
this, 

L  or  L,  =  47r2r2ni2Z 
is  a  very  rough  approximation. 

4.  Cylindrical  coil  with  a  single  layer  of  turns  whose  diameter  is  large  in  com- 
parison to  the  length  of  the  coil  (LORD  RAYLEIGH). 

,d        8r       1    ,      Z2     /.        8r    ,   1\  1 
:  47rrn2 1  log.  y  -  g  +^2r^(°ge  7  +  4/  j  ~  A  Ls 

The  following  equation  (CoFFiN353)  holds  almost  exactly  for  coils  of  only  one  layer 
of  turns  whose  radius  is  equal  to  the  coil  length  and  is  approximately  true  without 
great  error  even  if  the  coils  are  somewhat  longer. 

T  .  f  i       8r       1    .       Z2     I,       8r   .   1\  1      Z4  /.       8r       2\ 

L.=4*m*  jlog.T  ~2  +32^(logeT  +  4J   ~  1024  r «  (loge T  ~  3 ) 


10      x  J6  A0     &  _  109\   _       35        ^  A        8r      431\  1 


1   131072  "  r6  \    f>c  Z         120/        4194304 

In  these  equations  the  correction  factor  ALS  =  4arrn  (C  +  D)  (E.  B.  RosA353).     The 
values  of  C  and  D  are  given  in  the  table  following  below. 

5    Flat  spiral,  in  which  the  product  ng  <  0.5r  (r  is  here  the  radius  of  the  middle 
turn,  i.e.,  the  mean  radius)  (A.  EsAU353). 

Ls  =  lirr  \   n  flog.-  +  0.333)    +  n(n  -  1)  flog.  —  -  2  }    -  A  +  |^ 
I        \        P  I  \         9  I  8r2 

[  (loge 7  +  3 )  ("'(gl8~  X))  - 1]  1 c  g's- units 

6.  Rectangle  whose  sides  are  a  and  6,  of  wire  whose  radius  is  p : 

2ab  2ab 

Ls  =  4  {a  loge    -  --===—  +  6  loge 


r(a  +  Va2  +  62)  r(6  +  Va2  +  62) 

+  2(\/aM:r&2  -  a  -  6)} c.g.s.  units 

*  L  =  effective  coefficient  of  self-induction,  calculated  under  the  assumption  that 
the  current  flows  only  through  a  very  thin  surface  sheath  or  "skin." 


394 


WIRELESS  TELEGRAPHY 
Table  for  A  and  B 


n 

A 

B 

n 

A 

B 

1 

16 

354  4 

35,694 

2 

17 

415.8 

46,757 

3 

1.386 

8.315 

18 

482.8 

60,427 

4 

4.970 

43.296 

19 

555.5 

76,662 

5 

11.33 

140.82 

20 

634.2 

96,910 

6 

20.90 

366.95 

21 

718.9 

119,330 

7 

34.06 

794.73 

22 

809.7 

146,517 

8 

51.11 

1,499.55 

23 

906.6 

178,140 

9 

72.32 

2,590  .  62 

24 

1,009.8 

217,338 

10 

97.92 

4,187.55 

25 

1,119.4 

259,868 

11 

128.17 

6,572.94 

26 

1,235.4 

305,044 

12 

163.14 

9,769.47 

27 

1,357.9 

359,767 

13 

202.1 

14,042.1 

28 

1,487.1 

421,783 

14 

248.2 

19,532.2 

29 

1,618.1 

491,819 

15 

298.6 

26,740.1 

30 

1,765.4 

570,515 

Table  for  C 


2p 
9 

C 

2p 
9 

C 

2p 
9 

C 

1.00 

0.5568 

0.79 

0.3211 

0.59 

0  .  0292 

0.99 

0.5468 

0.78 

0.3084 

0.58 

0.0121 

0.98 

0.5367 

0.77 

0.2955 

0.57 

-0.0053 

0.97 

0.5264 

0.76 

0.2824 

0.56 

-0.0230 

0.96 

0.5160 

0.75 

0.2691 

0.55 

-0.0410 

0.95 

0.5055 

0.74 

0.2557 

0.54 

-0.0594 

0.94 

0.4949 

0.73 

0.2421 

0.53 

-0.0781 

0.93 

0.4842 

0.72 

0.2283 

0.52 

-0.0971 

0.92 

0.4734 

0.71 

0.2143 

0.51 

-0.1165 

0.91 

0.4625 

0.70 

0.2001 

0.50 

-0.1363 

0.90 

0.4515 

0.69 

0.1857 

0.45 

-0.2416 

0.89 

0.4403 

0.68 

0.1711 

0.40 

-0.3594 

0.88 

0.4290 

0.67 

0.1563 

0.35 

-0.4928 

0.87 

0.4176 

0.66 

0.1413 

0.30 

-0.6471 

0.86 

0.4060 

0.65 

0.1261 

0.85 

0.3943 

0.25 

-0.8294 

0.64 

0.1106 

0.20 

-1.0526 

0.84 

0.3825 

0.63 

0.0949 

0.15 

-1.3403 

0.83 

0.3705 

0.62 

0.0789 

0.10 

-1.7457 

0.82 

0.3584 

0.61 

0.0626 

0.81 

0.3461 

0.60 

0.0460 

0.80 

0.3337 

TABLES 
Table  for  D 


395 


n 

D 

n 

D 

n 

D 

1 

0  .  0000 

35 

0.3119 

300 

0.3343 

2 

0.1137 

40 

0.3148 

400 

0.3351 

3 

0.1663 

45 

0.3169 

500 

0.3356 

4 

0.1973 

50 

0.3186 

600 

0.3359 

5 

0.2180 

60 

0.3216 

700 

0.3361 

6 

0.2329 

70 

0.3239 

800 

0.3363 

7 

0.2443 

80 

0.3257 

900 

0.3364 

8 

0.2532 

90 

0.3270 

1000 

0.3365 

9 

0.2604 

100 

0.3280 

10 

0.2664 

125 

0.3298 

15 

0.2857 

150 

0.3311 

20 

0.2974 

175 

0.3321 

25 

0.3042 

200 

0.3328 

30 

0.3083 

396 


WIRELESS  TELEGRAPHY 


Table  VII.— Effective 

The  figures  give  the  resistance  of  1  m.  in  ohms,  under  the  assumption 

are  correct  within 


Diam.  of 
wire  in  mm. 

"Station- 
ary" current 

N  =  5  X  10< 
eye.  /sec. 
X  =  6000  m. 

N  =  1  X  105 
cyc./sec. 
X  =  3000  m. 

./V  =  1.5X105 
cyc./sec. 
X  =  2000  m. 

N  =  2XW5 
cyc./sec. 
X  =  1500  m. 

./V  =  2.5X105 
cyc./sec. 
X  =  1200  m. 

N  =  3X105 
cyc./sec. 
X  =  1000  m. 

0.2 

0.554 

0.55 

0.56 

0.56 

0.56 

0.56 

0.56 

0.4 

0.138 

0.139 

0.141 

0.143 

0.148 

0.152 

0.157 

0.6 

0.0615 

0.063 

0.067 

0.072 

0.078 

0.086 

0.093 

0.8 

0.0346 

0.0370 

0  .  0422 

0.0498 

0.056 

0.062 

0.067 

1 

0.0221 

0.0254 

0.0323 

0.0382 

0.0434 

0.0480 

0.052 

1.2 

0.0154 

0.0196 

0.0262 

0.0314 

0.0354 

0.0393 

0  .  0427 

1.4 

0.0113 

0.0164 

0.0221 

0.0263 

0.0298 

0.0331 

0.0359 

1.6 

0.00865 

0.0140 

0.0189 

0.0226 

0.0258 

0.0285 

0.0311 

1.8 

0.00683 

0.0123 

0.0169 

0.0199 

0.0226 

0.0251 

0.0273 

2 

0.00554 

0.0110 

0.0148 

0.0178 

0.0202 

0.0225 

0.0245 

2.2 

0.00457 

0.0098 

0.0133 

0.0159 

0.0182 

0.0203 

0.0221 

2.4 

0.00384 

0.0089 

0.0121 

0.0146 

0.0166 

0.0185 

0.0202 

2.6 

0.00328 

0.0081 

0.0111 

0.0134 

0.0153 

0.0171 

0.0186 

2.8 

0.00282 

0  .  0075 

0.0102 

0.0123 

0.0141 

0.0158 

0.0172 

3 

0.00246 

0.0069 

0.0095 

0.0115 

0.0132 

0.0147 

0.0160 

3.2 

0.00216 

0.0065 

0.0089 

0.0107 

0.0123 

0.0137 

0.0149 

3.4 

0.00192 

0.0061 

0.0083 

0.0101 

0.0116 

0.0129 

0.0141 

3.6 

0.00171 

0.0057 

0.0079 

0.0096 

0.0110 

0.0122 

0.0133 

3.8 

0.00153 

0.00535 

0.0074 

0.0090 

0.0103 

0.0114 

0.0125 

4 

0.00138 

0.0051 

0.0070 

0.0085 

0.0097 

0.0108 

0.0118 

4.2 

0.00125 

0.00479 

0.0066 

0.0080 

0.0092 

0.0103 

0.0112 

4.4 

0.00114 

0.00456 

0.0063 

0.0077 

0.0088 

0  .  0098 

0.0107 

4.6 

0.00105 

0.00438 

0.0061 

0.0074 

0.0085 

0.0094 

0.0103 

4.8 

0.000961 

0.00417 

0.0058 

0.0070 

0.0081 

0.0090 

0.0096 

5 

0.000886 

0.00400 

0.00555 

0.0067 

0.0077 

0.0086 

0.0094 

5.2 

0.000819 

0.00383 

0.0053 

0.0065 

0.0074 

0.0083 

0.0090s 

5.4 

0.000759 

0.00368 

0.0051 

0.0062 

0.0071s 

0  .  0080 

0.0086 

5.6 

0.000706 

0.00354 

0.00493 

0.0060 

0.0069 

0  .  0076 

0.0083 

5.8 

0.000658 

0  .  00341 

0.0047s 

0.0058 

0.00665 

0.0074 

0.0081 

6 

0.000615 

0.00330 

0.00458 

0.0056 

0.0064 

0.0071 

0.0078 

6.2 

0.000576 

0.00319 

0.00443 

0.0054 

0.0062 

0.0069 

0.0075s 

6.4 

0  .  000541 

0.00309 

0  .  00429 

0.0052 

0.0060 

0.0067 

0.0073 

6.6 

0.000508 

0.00299 

0.00415 

0.0050s 

0.0058 

0.0064s 

0.0071 

6.8 

0  .  000479 

0.00290 

0.00403 

0.00489 

0.0056 

0  .  0063 

0.0068s 

7 

0  .  000452 

0.00281 

0.00391 

0.00475 

0.0055 

0  .  0061 

0.0067 

7.2 

0.000427 

0.00272 

0.00379 

0.00461 

0.0053 

0.0059 

0.0064s 

7.4 

0.000404 

0.00265 

0.00369 

0.00448 

0.0051 

0  .  0058 

0  .  0063 

7.6 

0  .  000383 

0.00257 

0.00359 

0.00433 

0.0050 

0.0056 

0  .  0061 

7.8 

0.000364 

0.00251 

0.00350 

0  .  00426 

0  .  00488 

0.0055 

0.0059 

8 

0.000346 

0.00244 

0.00341 

0.00415 

0.00477 

0.0053 

0.0058 

TABLES 


397 


Resistance  of  Copper  Wires354 

that  the  specific  conductivity  a 
1  to  2  per  cent. 


57.5  X  1C-5  c.g.s.  units.      The  figures 


cyc./sec. 
X  =  857m. 

N  =  4X105 
cyc./sec. 
X  =  750  m. 

-$"  =  4.5X105 
cyc./sec. 
X  =  667  m. 

cyc./sec. 
X  =  600  m. 

AT  =  10<s 
cyc./sec. 
X  =  300m. 

cyc./sec. 
X  =  200  m. 

cyc./sec. 
X  =  150  m. 

cyc./sec. 
X  =  100  m. 

0.56 

0.56 

0.56s 

0.57 

0.61 

0.66 

0.73 

0.86 

0.163 

0.168 

0.175 

0.183 

0.245 

0.293 

0.328 

0.399 

0.099 

0.104 

0.110 

0.115 

0.156 

0.187 

0.213 

0.257 

0.072 

0.076 

0.079 

0.083 

0.110 

0.136 

0.157 

0.190 

0.0555 

0.062 

0.065 

0.069 

0.108 

0.124 

0.138 

0.151 

0.0456 

0.0489 

0.051 

0.053 

0.074 

0.089 

0.103 

0.125 

0.0384 

0.0405 

0  .  0452 

0.0450 

0.062 

0.076 

0.087 

0.106 

0.0333 

0.0353 

0  .  0372 

0.0394 

0.054 

0.066 

0.076 

0.093 

0.0294 

0.0314 

0.0331 

0.0345 

0.0480 

0.058 

0.067 

0.083 

0  .  0263 

0.0278 

0.0295 

0.0310 

0.0432 

0.053 

0.061 

0.074 

0.0238 

0.0254 

0.0267 

0.0280 

0.0392 

0.0479 

0.0551 

0.067 

0.0217 

0.0231 

0.0243 

0.0243 

0.0357 

0.0438 

0.0506 

0.062 

0.0200 

0.0212 

0.0224 

0.0236 

0.0329 

0.0400 

0  .  0469 

0.057 

0.0185 

0.0196 

0  .  0207 

0.0223 

0.0307 

0.0379 

0.0433 

0.053 

0.0172 

0.0183 

0.0193 

0.0204 

0.0287 

0.0350 

0.0405 

0.0497 

0.0161 

0.0171 

0.0180 

0.0190 

0.0267 

0.0328 

0.0381 

0  .  0459 

0.0151 

0.0160 

0.0170 

0.0178 

0.0252 

0.0309 

0.0357 

0.0431 

0.0143 

0.0154 

0.0160 

0.0168 

0.0239 

0.0293 

0.0337 

0.0407 

0.0134 

0.0143 

0.0151 

0.0159 

0.0225 

0.0277 

0.0314 

0.0386 

0.0127 

0.0136 

0.0140 

0.0151 

0.0214 

0  .  0263 

0.0300 

0.0366 

0.0121 

0.0128 

0.0136 

0.0145 

0.0205 

0  .  0246 

0.0285 

0.0349 

0.0115 

0.0123 

0.0130 

0.0138 

0.0196 

0.0235 

0.0272 

0.0331 

0.0111 

0.0118 

0.0125 

0.0131 

0.0187 

0.0225 

0.0260 

0.0317 

0.0106 

0.0113 

0.0120 

0.0127 

0.0177 

0.0216 

0.0250 

0.0304 

0.0101 

0.0108 

0.0115 

0.0124 

0.0169 

0  .  0207 

0.0240 

0.0292 

0.00975 

0.0104 

0.0111 

0.0116 

0.0162 

0.0199 

0.0229 

0.0281 

0.0093 

0.0100 

0.0106 

0.0112 

0.0156 

0.0192 

0.0220 

0.0271 

0.0091 

0.0097 

0.0102 

0.0108 

0.0152 

0.0185 

0.0213 

0  .  0261 

0.0087 

0.0093 

0.0099 

0.0104 

0.0146 

0.0176 

0.0203 

0.0252 

0  .  0084 

0.0090 

0.0095 

0.0101 

0.0141 

0.0172 

0.0199 

0.0243 

0.0081 

0.0087 

0.0092 

0.0098 

0.0136 

0.0167 

0.0192 

0  .  0235 

0.0079 

0.0084 

0.0089 

0.0095 

0.0132 

0.0162 

0.0186 

0  .  0228 

0.0076 

0.0081 

0  .  0086 

0.0092 

0.0128 

0.0157 

0.0181 

0.0221 

0.0074 

0.0078 

0  .  0083 

0  .  0088 

0.0123 

0.0151 

0.0175 

0.0214 

0.0071 

0  .  0076 

0.0081 

0  .  0085 

0.0120 

0.0148 

0.0172 

0.0208 

0.0070 

0.0074 

0.0079 

0  .  0083 

0.0117 

0.0143 

0.0166 

0.0203 

0.0067s 

0.0072 

0  .  0077 

0.0081 

0.0114 

0.0139 

0.0160 

0.0196 

0.0066 

0.0071 

0  .  0075 

0  .  0079 

0.0111 

0.0135 

0.0156 

0.0192 

0.0064 

0.0069 

0  .  0073 

0.0077 

0.0108 

0.0132 

0.0152 

0.0186 

0.0063 

0.0067 

0.0071 

0  .  0075 

0.0105 

0.0129 

0.0148 

0.0182 

398  WIRELESS  TELEGRAPHY 

Table  VIII. — Maximum  Diameter  of  Resistance  Waves355 

At  the  diameters  given  in  the  table  (in  millimeters)  the  resistance  differs  by  1 
per  cent,  from  the  D.C.  resistance.  If  the  difference  is  required  to  be  within  0.1 
per  cent.,  the  wire  diameter  must  not  be  more  than  about  half  (0.56,  to  be  exact) 
the  value  given  in  the  table.  A  wire  of  twice  the  diameter  in  the  table  (or  rather, 
1.78  times  the  diameter)  involves  a  10  per  cent,  difference. 


Material 

Conductivity 
in  c.g.s.  units 

Maximum  diameter  in  millimeters 

N  =  5X104 
cyc./sec. 
X  =  6000  m. 

N  =  2.5X105 
cyc./sec. 
X  =  1200  m. 

#  =  5X105 
cyc./sec. 
X  =  600  m. 

#  =  2.5X10« 
cyc./sec. 
X  =  120  m. 

Iron: 
Permeability  3000  
1000  
300  
100  
10  

10X10-5 
10X10-5 
10X10-5 
10X10-5 
10X10~5 
45X10-5 
57.5X10-5 
2X10~5 

2.4X10-5 

10x10-5 

0.08X10-5 
to 
0.4X10-5 
0.025X10-5 
1.06X10-5 

4.6X10-11 

0.019 

0.033 
0.059 
0.099 
0.33 
0.56 
0.49 
2.6 

2.4 

1.2 
13.2 

5.9 
23.6 
3.6 

175 

0  .  0084 
0.015 
0.027 
0.044 
0.15 
0.25 
0.22 
1.2 

1.1 

0.57 
5.9 

2.7 
10.6 
1.6 

78 

0.0060 

0.010 
0.018 
0.031 
0.10 
0.17 
0.15 
0.83 

0.75 

0.37 

4.2 

1.9 
7.5 
1.1 

55 

0.0027 
0  .  0046 
0  .  0084 
0.014 
0.046 
0.079 
0.0069 
0.37 

0.34 

0.17 
1.9 

0.84 
3.4 
0.51 

25 

Gold  

Copper  

Konstantan  

Manganin  1 

Nickelm      / 
Platinum   .... 

Graphite  *  

Carbon  (arc-lamp) 

Mercury  

Concentrated  CuSO4  solu- 
tion   

*  For  a  rectangular  section,  the  figures  give,  with  close  approximation,  the  maxi- 
mum value  which  the  largest  diameter  may  have,  if  the  difference  between  effective 
and  D.C.  resistance  is  to  be  not  greater  than  1  per  cent. 


TABLES 


399 


Table  IX. — Gap  Lengths  and  Corresponding  Minimum  Discharge  Voltages64 

For  short  gaps: 


0        O.I      0.2      0.3      04     0.5     0.6      0.7      0.8      0.9       1       1.1      1.2     1.3      1.4 
Maximum  Gap  Length  in  cm. 

FIG.  468. 


1.5 


400 


WIRELESS  TELEGRAPHY 


For  longer  gaps: 


1 L | >  _ 


1  234  567 

Maximum  Gap  Length  in  cm. 

FIG.  469. 

In  these  figures  (468  and  469),  r  is  the  radius  of  the  spherical  electrodes;  the 
dotted  curve  in  Fig.  469  refers  to  very  shallow  bowl-shaped  electrodes. 

The  values  plotted  are  the  normal' discharge  or  ignition  voltages,  i.e.,  the  voltages 
which  are  just  sufficient  for  the  discharge  to  take  place  in  air  having  no  appreciable 
ionization. 

The  values  of  Fig.  468  are  due  to  A.  HEYDWEiLLER,64  those  of  Fig.  469  to  C.  MtiL- 
LER56  (for  the  short  gap  lengths)  and  E.  HuPKA64  and  those  for  the  dotted  curve  in  Fig. 
469  are  due  to  W.  WEiCKEB;64  barometric  pressure  745  mm.,  temperature  about  18° 
C.  The  figures  for  Fig.  468  were  determined  in  dry  air  at  18°  C.  temperature  and  745 
mm.  pressure;  an  increase  of  8  mm.  pressure  and  a  decrease  of  3°  temperature  cause 
an  increase  of  1  per  cent,  in  the  voltages. 


TABLES 


401 


Table  X.  —  Determination  of  Percentage  Coupling 

According  to  Art.  87,  the  degree  of  coupling  is 


N 


1 


In  the  following  table,  the  degree  of  coupling  is  given  in  percentage;  thus  for 
Kf  =  0.02  the  figure  given  is  2  (per  cent.). 


I 

II 

III 

^0^ 

x       Ni 

Percentage 
coupling 

X11        N 
*-°V' 

Percentage 
coupling 

ALor^7 
X11        N1 

Percentage 
coupling 

0.999 

0.20 

1.001 

0.20 

1.001 

0.100 

0.998 

0.40 

1,002 

0.40 

1.002 

0.200 

0.997 

0.60 

1.003 

0.60 

1.003 

0.299 

0.996 

0.80 

1.004 

0.80 

1.004 

0.398 

0.995 

1.00 

1.005 

1.00 

1.005 

0.498 

0.994 

1.20 

1.006 

1.20 

1.006 

0.596 

0.993 

1.40 

1.007 

1.40 

1.007 

0.695 

0.992 

1.59 

1.008 

1.61 

1.008 

0.799 

0.991 

1.79 

1.009 

1.81 

1.009 

0.897 

0.99 

1.99 

1.01 

2.01 

1.01 

0.99 

0.98 

3.96 

1.02 

2.04 

1.02 

1.98 

0.97 

4.91 

1.03 

6.09 

1.03 

2.97 

0.96 

7.84 

1.04 

8.16 

1.04 

3.92 

0.95 

9.75 

1.05 

10.2 

1.05 

4.87 

0.94 

11.6 

1.06 

12.4 

1.06 

5.82 

0.93 

13.5 

1.07 

14.5 

1.07 

6.76 

0.92 

15.4 

1.08 

16.6 

1.08 

7.68 

0.91 

17.2 

1.09 

18.8 

1.09 

8.60 

0.90 

19.0 

1.10 

21.0 

1.10 

9.50 

0.89 

20.8 

1.11 

23.2 

1.11 

10.4 

0.88 

22.6 

1.12 

25.4 

1.12 

11.3 

0.87 

24.3 

1.13 

27.7 

1.13 

12.2 

0.86 

26.0 

1.14 

30.0 

1.14 

13.0 

0.85 

27.8 

1.15 

32.2 

1.15 

13:9 

2G 


402 


WIRELESS  TELEGRAPHY 
Table  X.     (Continued) 


1 

II 

ill 

XJ         N 
^°rNI~ 

Percentage 
coupling 

X11         N 
^°r^ 

Percentage 
coupling 

XJ         N11 

xIj€V 

Percentage 
coupling 

.    0.84 

29.4 

1.16 

34.6 

1.16 

14.7 

0.83 

31.1 

1.17 

36.9 

1.17 

15.6 

0.82 

32.8 

1.18 

39.2 

1.18 

16.4 

0.81 

34.4 

1.19 

41.6 

1.19 

17.2 

0.80 

36.0 

1.20 

44.0 

1.20 

18.0 

0.79 

37.6 

1.21 

46.4 

1.21 

18.8 

0.78 

39.2 

1.22 

48.8 

1.22 

19.6 

0.77 

40.7 

1.23 

51.3 

1.23 

20.4 

0.76 

42.2 

1.24 

53.8 

1.24 

21.2 

0.75 

43.8 

1.25 

56.2 

1.25 

22.0 

0.74 

45.2 

1.26 

58.8 

1.26 

22.7 

0.73 

46.7 

1.27 

61.3 

1.27 

23.5 

0.72 

48.2 

1.28 

63.8 

1.28 

24.2 

0.71 

49.6 

1.29 

66.4 

1.29 

24.9 

0.70 

51.0 

1.30 

69.0 

1.30 

25.6 

0.69 

52.4 

.31 

26.4 

0.68 

53.8 

.32 

27.1 

0.67 

55.1 

.33 

27.8 

0.66 

56.4 

.34 

28.5 

0.65 

57.8 



.35 

29.1 

0.64 

59.0 

.36 

29.8 

0.63 

60.3 

.37 

30.5 

0.62 

61.6 

.38 

31.1 

0.61 

62.8 

.39 

31.8 

0.60 

64.0 

.40 

32.4 

.41 

33.0 

.42 

33.7 

.43 

34.3 

.... 

.44 

34.9 





.45 

35.5 

.46 

36.1 

.... 

.47 

36.7 

1.48 

37.3 

1.49 

37.9 



1.50 

38.5 

1.55 

41.2 

1.60 

43.8 

1.65 

46.3 

. 

1.70 

48.6 





1.75 

50.7 

1.80 

52.8 

.... 

1.85 

54.8 

1.90 

56.6 

1.95 

58.4 

2.00 

60.0 

TABLES 


403 


Table  XL—Resonance  Curve  of  the  Current  Effect  [Art.  740] 

Let  di  and  dz  represent  the  decrements  of  the  primary  and  secondary  circuits, 
respectively,  72e//  the  current  effect  in  the  secondary  circuit  and  I\  «//  the  same  at 
resonance  between  the  two  circuits.  The  resonance  curve  is  obtained  by  plotting 
the  values  of  the  ratio  /2e//  :  I\  eff  as  ordinates,  y,  and  the  values  of  the  dissonance 

between  the  two  circuits  as  abscissae.     Let  x  =          — -r  the  meaning  of  x\  and  Xz 
being  obvious  from  Fig.  470.     Then  : 

di  +  dz  =  x  X  27r 

=  xA 
The  assumptions  are : 

1.  z<  1.0. 

2.  di  +  d2<27r  and 

3.  Very  loose  coupling  between  primary  and  secondary  circuits. 

In  the  following  table  the  value  of  A  and  log  A  is  given  for  different  values  of  y. 


y 

log  A 

A 

y 

log  A 

A 

0.998 

2.1472 

140 

0.958 

1.4773 

30.0 

0.996 

1.9963 

99.2 

0.956 

1.4667 

29.3 

0.994 

1.9078 

80.9 

0.954 

1.4565 

28.6 

0.992 

1  .  8449 

70.0 

0.952 

1.4469 

28.0 

0.990 

1.7960 

62.5 

0.950 

1.4376 

27.4 

0.988 

1.7560 

57.0 

0.945 

1.4157 

26.0 

0.986 

1.7221 

52.7 

0  .  940 

1.3956 

24.9 

0.984 

1.6926 

49.3 

0.935 

1.3771 

23.8 

0.982 

1.6666 

46.4 

0.930 

1  .  3599 

22.9 

0.980 

1.6433 

44.0 

0.925 

1.3437 

22.1 

0.978 

.6221 

41.9 

0.920 

1.3285 

21.3 

0.976 

.6028 

40.1 

0.915 

1.3142 

20.6 

0.974 

.5850 

38.5 

0.910 

.3006 

20.0 

0.972 

.5684 

37.0 

0.905 

.2876 

19.4 

0.970 

.5530 

35.7 

0.900 

.2753 

18.  85 

0.968 

.5386 

34.5 

0.89 

.2522 

17.9 

0.966 

.5249 

33.5 

0.88 

.2308 

17.0 

0.964 

.5121 

32.5 

0.87 

.2110 

16.3 

0.962 

1.4994 

31.6 

0.86 

.1924 

15.6 

0.960 

1.4883 

30.8 

0.85 

.1748 

15.0 

404 


WIRELESS  TELEGRAPHY 


Table  XI.     (Continued) 


y 

log  A 

i 

A 

y 

log  A 

A 

0.84 

.1583 

14.4 

0.39 

0.7011 

5.02 

0.83 

.1425 

13.9 

0.38 

0.6919 

4.92 

0.82 

.1274 

13.4 

0.37 

0.6827 

4.82 

0.81 

.1130 

13.0 

0.36 

0.6734 

4.71 

0.80 

.0993 

12.6 

0.35 

0.6638 

4.61 

0.79 

.0859 

12.2 

0.34 

0.6542 

4.51 

0.78 

.0730 

11.8 

0.33 

0.6444 

4.41 

0.77 

.0606 

11.5 

0.32 

0.6345 

4.31 

0.76 

1.0485 

11.2 

0.31 

0.6245 

4.21 

0.75 

1.0367 

10.9 

0.30 

0.6142 

4.11 

0.74 

1.0253 

10.6 

0.29 

0.6033 

4.01 

0.73 

1.0141 

10.3 

0.28 

0.5932 

3.92 

0.72 

1.0032 

10.1 

0.27 

0.5823 

3.82 

0.71 

0.9931 

9.84 

0.26 

0.5711 

3.72 

0.70 

0.9822 

9.60 

0.25 

0.5597 

3.63 

0.69 

0.9719 

9.37 

0.24 

0.5479 

3.53 

0.68 

0.9619 

9.16 

0.23 

0.5358 

3.43 

0.67 

0.9518 

8.95 

0.22 

0  .  5234 

3.34 

0.66 

0.9422 

8.75 

0.21 

0.5105 

3.24 

0.65 

0.9326 

8.56 

0.20 

0.4971 

3.14 

0.64 

0  .  9230 

8.38 

0.19 

0.4834 

3.04 

0.63 

0.9137 

8.20 

0.18 

0.4690 

2.94 

0.62 

0.9045 

8.03 

0.17 

0.4539 

2.84 

0.61 

0.8953 

7.86 

0.16 

0.4381 

2.74 

0.60 

0.8862 

7.69 

0.15 

0.4216 

2.64 

0.59 

0.8772 

7.54 

0.14 

0.4040 

2.54 

0.58 

0.8683 

7.38 

0.13 

0.3854 

2.43 

0.57 

0.8594 

7.23 

0.12 

0.3656 

2.32 

0.56 

0  .  8505 

7.09 

0.11 

0.3442 

2.21 

0.55 

0.8418 

6.95 

0.10 

0.3211 

2.09 

0.54 

0.8330 

6.81 

0.09 

0.2958 

1.98 

0.53 

0.8243 

6.67 

0.08 

0.2679 

1.85 

0.52 

0.8156 

6.54 

0.07 

0.2365 

1.72 

0.51 

0.8069 

6.41 

0.06 

0.2008 

1.59 

0.50 

0.7982 

6.28 

0.05 

0.1588 

1.44 

0.49 

0.7895 

6.16 

0.04 

0.1081 

1.28 

0.48 

0.7808 

6.04 

0.03 

0.0434 

1.10 

0.47 

0.7721 

5.92 

0.02 

0.9531-1 

0.90 

0.46 

0.7634 

5.80 

0.01 

0.8004-1 

0.63 

0.45 

0.7546 

5.68 

0.44 

0.7459 

5.57 

0.43 

0.7370 

5.46 

0.42 

0.7281 

5.35 

0.41 

0.7192 

5.24 

0.40 

0.7102 

5.13 

TABLES 
Table  XII. — Resonance  Sharpness  p  = 


405 


^-y-  [Art.  700] 
~r  #2 


di  +  dz 

p 

di  +  d* 

p 

di  +d2 

P 

di  +  d2 

P 

0.010 

628 

0.033 

190 

0.056 

112 

0.079 

79.4 

0.011 

571 

0.034 

185 

0.057 

110 

0.080 

78.5 

0.012 

524 

0.035 

179.5 

0.058 

108 

0.013 

483 

0.059 

106.5 

0.081 

77.6 

0.014 

449 

0.036 

174.5 

0.060 

105 

0.082 

76.6 

0.015 

419 

0.037 

170 

0.083 

75.7 

0.038 

165 

0.061 

103 

0.084 

74.8 

0.016 

393 

0.039 

161 

0.062 

101 

0.085 

73.9 

0.017 

370 

0.040 

157 

0.063 

99.7 

0.018 

349 

0.064 

98.2 

0.086 

73.1 

0.019 

331 

0.041 

153 

0.065 

96.7 

0.087 

72.2 

0.020 

314 

0.042 

150 

0.088 

71.4 

0.043 

146 

0.066 

95.2 

0.089 

70.6 

0.021 

299 

0.044 

143 

0.067 

93.8 

0.090 

69.8 

0.022 

286 

0.045 

140 

0.068 

92.4 

0.023 

273 

0.069 

91.1 

0.091 

69.0 

0.024 

262 

0.046 

137 

0.070 

89.8 

0.092 

68.3 

0.025 

251 

0.047 

134 

0.093 

67.6 

0.048 

131 

0.071 

88.5 

0.094 

66.8 

0.026 

242 

0.049 

128 

0.072 

87.3 

0.095 

66.1 

0.027 

233 

0.050 

126 

0.073 

86.1 

0.028 

224 

0.074 

85.0 

0.096 

65.5 

0.029 

217 

0.051 

123 

0.075 

83.8 

0.097 

64.8 

0.030 

209 

0.052 

121 

0.098 

64.1 

0.053 

118.5 

0.076 

82.7 

0.099 

63.5 

0.031 

203 

0.054 

116 

0.077 

81.6 

0.100 

62.8 

0.032 

196 

0.055 

114 

0.078 

80.5 

Table  XIII.—  The  Radiation  Resistance  of  Antennae 

According  to  Art.  lOOc,  the  radiation  resistance,  Rz,  of  an  antenna  whose  height 
is  h  and  form  factor  is  a  and  which  is  erected  on  ground  of  high  conductivity,  is  given 
by: 


=  «2  X  1607T2          ohms. 


In  the  following  table  the  different  values  of  the  expression  160ir 


(—  J 


are  given. 


Hence  the  radiation  resistance  in  ohms  is  found  by  multiplying  the  figure  given  in 
the  table  by  the  square  of  the  form  factor  of  the  antenna. 


406 


WIRELESS  TELEGRAPHY 


Wave  length  X  in  meters 

300 

400 

500 

600 

700 

800 

900 

1000 

1500 

2000 

10 

1.75s 

0.987 

0.632 

0.439 

0.332 

0.247 

0.195 

0.158 

0.0702 

0.0395 

15 

3.95 

2.22 

1.42 

0.987 

0.725 

0.555 

0.439 

0.355 

0.158 

0.088 

20 

7.02 

3.95 

2.53 

1.75s 

1.29 

0.987 

0.780 

0.632 

0.281 

0.158 

25 

11.0 

6.17 

3.95 

2.74 

2.01 

1.54 

1.22 

0.987 

0.439 

0.247 

30 

15.8 

8.88 

5.68s 

3.95 

2.90 

2.22 

1.75 

1.42 

0.634 

0.355 

35 

21.5 

12.1 

7.74 

5.37s 

3.95 

3.02 

2.39 

1.93 

0.860 

0.484 

40 

28.1 

15.8 

10.1 

7.02 

5.16 

3.95 

3.12 

2.53 

1.12 

0.632 

45 

35.5 

20.0 

12.8 

8.88 

6.53 

5.00 

3.95 

3.20 

1.42 

0.800 

50 

43.9 

24.7 

15.8 

11.0 

8.06 

6.17 

4.87 

3.95 

1.75 

0.987 

£ 

3     55 

53.1 

29.8 

19.1 

13.3 

9.79 

7.46 

5.90 

4.78 

2.12 

1.19 

1     60 

63.2 

35.5 

22.7 

15.8 

11.6 

8.88 

7.02 

5.68s 

2.53 

1.42 

d     65 

74.1 

41.7 

26.7 

18.5 

13.6 

10.4 

8.24 

6.67 

2.96s 

1.67 

•s     70 

86.0 

48.4 

30.9s 

21.5 

15.8 

12.1 

9.55 

7.74 

3.44 

1.93s 

§     75 

98.7 

55.4 

35.5 

24.7 

18.1 

13.9 

11.0 

8.88 

3.95 

2.22 

•g     80 

63  2 

40  4 

28  1 

20.6 

15  8 

12.5 

10.1 

4  49 

2  53 

«     85 

71.3 

45.6 

31.7 

23.3 

17.8 

14.1 

11.4 

5.07 

2.85 

'3     90 

.... 

80.0 

51.2 

35.5 

26.1 

20.0 

15.8 

12.8 

5.686 

3.20 

•5     95 

89.1 

57.0 

39.6 

29.1 

22.3 

17.6 

14.2s 

6.33s 

3.56 

;§>  100 

98.7 

63.2 

43.9 

32.2 

24.7 

19.5 

15.8 

7.02 

3.95 

'3 

'^  110 

76.4 

53.1 

39  0 

29.8s 

23.6 

19.1 

8.49 

4.78 

120 

90.  96 

63.2 

46.4 

35.5 

28.1 

22.7 

10.1 

5.68s 

130 

74.1 

54.5 

41.7 

32.9 

26.7 

11.9 

6.67 

140 

86.0 

63.2 

48.4 

38.2 

30.9s 

13.8 

7.74 

150 

98.7 

72.5 

55.4 

43.9 

35.5 

15.8 

8.88 

160 

82.5 

63.2 

49.9 

40.4 

18.0 

10.1 

170 

93.1 

71.3 

56.3 

45.6 

20.3 

11.4 

180 

80.0 

63.2 

51.2 

22.7 

12.8 

190 

89.1 

70.4 

57.0 

25.3 

14.2 

200 

98.7 

78.0 

63.2 

28.1 

15.8 

TABLES 


407 


Wave  length  X  in  meters 

2500 

3000 

3500 

4000 

4500 

5000 

5500 

6000 

6500 

7000 

10 

0.0253 

0.0175s 

0.0129 

0.00987 

0.00780 

0.00632 

0.0052 

0.00439 

0.0037 

0.00332 

15 

0.0568 

0.0395 

0.0290 

0.0222 

0.0176 

0.0142 

0.0117 

0.00987 

0.0084 

0.00725 

20 

0.101 

0.0702 

0.0516 

0.0395 

0.0312 

0.0253 

0.0209 

0.0175s 

0.0149s 

0.0129 

25 

0.158 

0.110 

0.0806 

0.0617 

0.0487 

0.0395 

0.0326 

0.0274 

0.0234 

0.0210 

30 

0.227 

0.158 

0.116 

0  .  0888 

0  .  0702 

0.0568s 

0.0470 

0.0395 

0.0336 

0.0290 

35 

0.309s 

0.215 

0.158 

0.121 

0.0955 

0.0774 

0  .  0639s 

0.0537s 

0.0458 

0.0395 

40 

0.404 

0.281 

0.206 

0.158 

0.125 

0.101 

0.0835 

0.0702 

0.0598 

0.0516 

45 

0.512 

0.355 

0.261 

0.200 

0.158 

0.128 

0.106 

0  .  0888 

0.0757 

0.0653 

50 

0.632 

0.439 

0.322 

0.247 

0.195 

0.158 

0.130s 

0.110 

0.0934 

0.0806 

1     55 

0.764 

0.531 

0.390 

0.298s 

0.236 

0.191 

0.158 

0.133 

0.113 

0.0979 

S    60 

0.910 

0.632 

0.464 

0.355 

0.281 

0.227 

0.188 

0.158 

0.134 

0.116 

;     65 

1.07 

0.741 

0.544 

0.417 

0.329 

0.267 

0.221 

0.185 

0.158 

0.136 

.a  70 

1.2.4 

0.860 

0.631 

0.484 

0.382 

0.309s 

0.256 

0.215 

0.183 

0.158 

g     75 

1.42 

0.987 

0.725 

0.554 

0.439 

0.355 

0.294 

0.247 

0.210 

0.181 

a 

•§     80 

1.62 

1.12 

0.825 

0.632 

0.499 

0.404 

0.334 

0.281 

0.239 

0.206 

§     85 

1.83 

1.27 

0.931 

0.713 

0.563 

0.456 

0.377 

0.317 

0.270 

0.233 

•S     90 

2.05 

1.42 

1.04 

0.800 

0.632 

0.512 

0.423 

0.355 

0.303 

0.261 

Z    95 

2.28 

1.58 

1.16 

0.891 

0.704 

0.570 

0.471 

0.396 

0.337 

0.291 

§100 

2.53 

1.75s 

1.29 

0.987 

0.780 

0.632 

0.522 

0.439 

0.374 

0.322 

'3 

W  110 

3.06 

2.12 

1.56 

1.19 

0.943s 

0.764 

0.632 

0.531 

0.452 

0.390 

120 

3.64 

2.53 

1.86 

1.42 

1.12 

0.910 

0.752 

0.632 

0.538 

0.464 

130 

4.27 

2.96s 

2.18 

1.67 

1.32 

1.07 

0.882 

0.741 

0.631 

0.545 

140 

4.95 

3.44 

2.53 

1.93 

1.53 

1.24 

1.02 

0.860 

0.732 

0.632 

150 

5.68s 

3.95 

2.90 

2.22 

1.76 

1.42 

1.17 

0.987 

0.840 

0.725 

160 

6.47 

4.49 

3.30 

2.53 

2.00 

1.62 

1.34 

1.12 

0.957 

0.825 

170 

7.30 

5.07 

3.72s 

2.85 

2.25 

1.83 

1.51 

1.27 

1.08 

0.931 

180 

8.19 

5.68s 

4.18 

3.20 

2.53 

2.05 

1.69 

1.42 

1.21 

1.04 

190 

9.12 

6.33s 

4.65 

3.56 

2.81s 

2.28 

1.88s 

1.58 

1.35 

1.16 

200 

10.1 

7.02 

5.16 

3.95 

3.12 

2.53 

2.09 

1.75 

1.49s 

1.29 

BIBLIOGRAPHY  AND  NOTES  ON  THEORY 

1  Works  covering  the  general  subject  of  radio-telegraphy: 

a.  F.  ANDERLE,  Lehrbuch  der  drahtlosen  Telegraphic  und  Telephonic,  Leipzig 

and  Vienna,  1912. 
fe.  J.  ERSKINE-MURRAY,  A  handbook  of  wireless  telegraphy,  its  theory  and 

practice.     3d  Edit.,  London,  1911. 

c.  J.  A.   FLEMING,   The  principles  of  electric  wave  telegraphy.     2d  Edit., 
London,  Longmans,  Green  &  Co.,  1910. 

d.  G.  W.  PIERCE,  Principles  of  wireless  telegraphy.     New  York,  McGraw-Hill 
Book  Co.,  1910. 

e.  H.  REIN,  Radiotelegraphisches  Praktekum.     2d  Edit.,   Berlin,   Springer, 
1912. 

/.    C.  TISSOT,  Manuel  elementaire  de  telegraphic  san  fil.     Paris,  1912. 

g.  A.  ZAMMARCHI,  La  telegraphia  senza  fili  di  Guglielmo  Marconi.     Bergamo, 

1904.     (Of  historical  interest  only.) 
h.  J.  ZENNECK,  Elektromagnetische  Schwingungen  und  drahtlose  Telegraphic. 

Stuttgart,  1905." 
i.    Theoretical:  C.  TISSOT,  Les  oscillations  electriques.     Paris,  1910. 

2  Special  arrangements  for  the  use  of  the  Braun  tube  with  rapid  oscillations:  L. 

MANDELSTAM,  Jahrb.,  1,  124,  1908.  (The  same  method  employed  by  D. 
ROSCHANSKY,  Ann.  Phys.,  36,  281,  1911.)  H.  HAUSRATH,  Phys.  Zeitschr.,  12, 
1044,  1911;  also  Jahrb.,  6,  185,  1912.  K.  ORT,  Jahrb.,  6,  119,  1912.  E.  L. 
CHAFFEE,  Proc.  Amer.  Acad.  Arts  and  Sciences,  47,  311  et  seq.,  1911. 

3  W.  FEDDERSEN,  Pogg.  Ann.,  113,  437,  1861;  also  116,  132,  1862.     Also  see  Beriichte 

der  sachs.  Ges.  der  Wissenschaften,  61,  151,  1909.  For  frequency  determina- 
tions, the  method  of  HEMSALECH  (C.  R.,  132,  912,  1901,  illumination  of  a  slit 
by  the  spark)  gives  particularly  suitable  pictures. 

4  E.  GEHRKE,  Verhandl.  Physik.  Ges.,  6,  176,  1904;  Zeitschr.  f.  Instrumentenkunde, 

15,  33,  278,  1905.     Reproductions  by  means  of  the  incandescent  lamp  oscillo- 
graph: H.  DIESSELHORST,  Ber.  phys.  Ges.,  5,  320,  1907;  6,  306,  1908;  ETZ, 
29,  703,  1908. 
6  W.  THOMSON,  Phil.  Mag.  (4),  6,  593,  1855. 

6  J.  A.  FLEMING,  Elecn.,  63,  459,  1909.     H.  ANDERSON,  Phys.  Rev.,  34,  34,  1912. 

7  M.  WIEN,  Phys.  Zeitschr.,  11,  282  et  seq.,  1910.     H.  RIEGGER,  Diss.  Strassburg, 

1911;  Jahrb.,  5,  35,  1911.  For  explanation,  see  D.  ROSCHANSKY,  Phys. 
Zeitschr.,  11,  1177,  1910. 

8  In  regard  to  more  recent  work,  see  H.  DIESSELHORST,  Jahrb.,  1,  263,  1908. 

9  To  be  more  accurate,  this  should  be  ^  L/o2,  the  energy  transferred  in  a  half  cycle  (see 

E.  COHN,  Das  elektromagnetische  Feld,  p.  360.     Leipzig,  1900). 

10  F.  RICHARZ  and  W.  ZIEGLER,  Ann.  Phys.,  1,  468,  1900.     J.  ZENNECK,  Ann.  Phys., 

13,  822,  1904. 

11  This  refers  to  gaps  in  air.     According  to  E.  L.  CHAFFEE,  2  a  straight  line  amplitude 

curve  is  also  obtained  with  aluminium  electrodes  in  hydrogen  and  with  carbon 
electrodes  in  air. 

12  A.  HEYDWEILLER,  Ann.  Phys.,   19,  649,   1906;  25,  48,   1908.     W.  STUFF,  Diss. 

Munster,  1907.     H.  BARKHAUSEN,  Phys.  Zeitschr.,  8,  624,  1907. 

408 


BIBLIOGRAPHY  AND  NOTES  ON  THEORY  409 

13  That  is,  Rg  is  defined  by 


=  the  energy  consumed  during  one  spark  discharge. 

14  This  arrangement  was  proposed  by  MARESCA  (Phys.  Zeitschr.,  4,  9,  1902),  and  the 

method,  in  the  form  described  in  the  text,  by  K.  SIMONS  (Ann.  Phys.,  13,  1044, 
1904). 

15  Determinations  of  the  gap  resistance  or  decrement:  G.  REMPP,  Diss.  Strassburg 

and  Ann.  Phys.,  17,  627,  1905.  (His  values,  particularly  for  gaps  over  6  mm. 
long,  are  too  high  as  the  effect  of  brush  discharge  was  not  understood  at  that 
time.)  H.  RAUSCH  VON  TRAUBENBERG  and  W.  HAHNEMANN,  Phys.  Zeitschr., 
8,  498,  1907.  K.  E.  F.  SCHMIDT,  Phys.  Zeitschr.,  8,  617,  1907.  C.  RICHTER, 
Phys.  Zeitschr.,  10,  703,  1909.  M.  WIEN,  Ber.  physik.  Ges.,  12,  736,  1910; 
Ann.  Phys.,  29,  679  et  seq.,  1909.  W.  F.  ZORN,  Jahrb.,  4,  269  et  seq.,  382  et  seq., 
1911. 


also 
whence 


T         Fo 
•*o   =      F 


17  M.  WIEN,  Ann.  Phys.,  29,  679  et  seq.,  1909. 

18  Measurements  by   W.   EICKHOFF   at   the  physikalisches   Institut   Braunschweig 

(see  Phys.  Zeitschr.,  8,  497,  1907). 

19  D.  ROSCHANSKY,  Jahrb.,  3,  81,  1909. 

20  W.  EICKHOFF,  Phys.  Zeitschr.,  8,  494,  1907.     In  regard  to  the  voltage  conditions 

in  series  spark  gaps  see  P.  NORDMEYER,  Jahrb.,  3,  334  et  seq.,  1910. 

21  B.  MONASCH,  Ann.  Phys.,  22,  905,  1907.     W.  HAHNEMANN  and  L.  ADELMANN, 

ETZ,  1907,  988,  1010.  M.  WiEN.17  J.  A.  FLEMING  and  G.  B.  DYKE,  EL, 
66,  658  et  seq.,  1911.  L.  W.  AUSTIN,  Jahr.  5,  420,  1912.  According  to  AUSTIN 
the  glass  furnished  by  the  Wireless  Specialty  Apparatus  Co.  is  particularly 
good. 

22  This  phenomenon  is  identical  with  the  "corona"  of  high-tension  transmission  cir- 

cuits (see,  e.g.,  W.  PETERSEN,  Hochspannungstechnik,  p.  308  et  seq.,  Stuttgart, 
1911). 

23  A.  MEISSNER,  Jahrb.,  3,  57  et  seq.,  1909. 

24  Detailed  treatment  in  EMS,  p.  498  et  seq.,  743  et  seq.  (Note  1  h) 

26  According  to  F.  HARMS  (Ann.  Phys.,  23,  60,  1907)  the  velocity  of  propagation  and 
hence  also  the  frequency  are  less  for  wires  with  an  insulating  sheath. 

26  M.  ABRAHAM,  Wied.  Ann.,  66,  435  et  seq.     F.  HACK,  Ann.  PhyS.,  14,  539,  1904. 

The  field  of  an  oscillator  whose  current  amplitude  is  the  same  at  all  points 
(a  =  1)  has  been  calculated  by  H.  HERTZ,  Wied.  Ann.,  36,  1,  1888;  Ges. 
Werke  II,  45. 

27  F.  HACK,  Ann.  Phys.,  18,  634,  1905. 

28  Detailed  treatment  of  oscillations  in  coils,  P.  DRUDE,  Ann.  Phys.,  9,  593,  1902. 

J.  A.   FLEMING.1 

29  M.  WIEN,  Jahrb.,  1,  474,  1908. 

30  G.  SBIBT,  ETZ,  1902,  411.     Also  experiments  in  the  physikal.  Inst.  Braunschweig. 


410  WIRELESS  TELEGRAPHY 

31  This   follows   from   the   well-known    "telegraph  equation"  of  KIRCHHOFF.     See, 

e.g.,  B.  C.  TissoT.1 

32  Experimental  method  for  determining  the  current  anti-node  in  an  open  oscillator, 

A.  ESAU,  Phys.  Zeitschr.,  13,  495,  1912. 

33  If  the  current,  /,  is  of  the  form 

7  =  /o  sin  wt, 
<;hen  at  a  distance  r, 

E  =  Eo  cos  I  cot  -  —J  and  M  =  M0  cos  I  tat ~ 

(The  algebraic  sign  before  E  and  M  being  in  accordance  with  Fig.  37,  p.  35, 
/  is  taken  positive  in  direction  from  A  to  B.) 

34  M.  ABRAHAM,  Theorie  der  Elektrizitat  II,  p.  286.     Leipzig,  1905.     Application  to 

various  forms  of  oscillators  by  A.  MONTEL,  Lum.  el.,  6,  199,  207,  1909. 


35  I0  =  £  I    I0dx  (I  =  length  of  oscillator). 

35  In  this  case,  we  have  for  each  half  of  the  oscillator, 

/o   =  |/o|  A   -  ~ 


1    I 

2j  o 


1    I  I0dx 


l/ol  2 

where  x  =  distance  from  middle  of  oscillator.     Hence 
37  Here 

,  .  ,    .  TTX 

-/O    =    |/0|  COS   -- 


370  This  follows  directly  from  the  fact   that   the   radiation  S  =  ^  [2£Af  ]  in  which 

[EM]  is  the  product  of  the  vectors  E  and  M  . 

38  This  is  easily  arrived  at  from  M.  ABRAHAM,34  p.  301  et  seq. 

39  R.  RUDENBERG,  Ann.  Phys.,  25,  446,  1908.     Also  see  H.  BARKHAUSEN,  Jahrb.,  2, 

40,  1908.     P.  BARRECA,  Jahrb.,  4,  31  et  seq.,  1910. 

40  All  difficulties  which  otherwise  are  apt  to  be  encountered  in  coupled  circuits  can  be 

avoided  by  proceeding  as  follows:  At  any  point  x  on  the  oscillator,  the  current 


Furthermore  let  the  energy  consumed  per  second  as  heat  be  expressed  by 


|  RW  x  I*dx  =  I/1,*  | 

and  the  following  inch 
d,  so  far  as  the  oscillati 

j  LMl*dx  =  H\I\2  I 


(the  integral  in  this  and  the  following  includes  the  entire  oscillator),  the  energy 
of  the  magnetic  field,  so  far  as  the  oscillations  are  concerned,  by 


BIBLIOGRAPHY  AND  NOTES  ON  THEORY  411 

and  the  energy  of  the  electrical  field  by 


Moreover 


I  CWV*dx  =  KIF12  I  C^v 


The  differential  equation  of  the  oscillation  is  then : 

/  2    C      CD  2d  11/2    f  L(l)  2  1          I 

J  *"     2       J  f5i     2 

or 

../• 


r  r 

J  R^f(xydx  +  ^  J 


=  0 


This  can  be  reduced  to  the  same  form  as  pertains  to  the  natural  oscillations  of  a 
condenser  circuit,  viz.: 

1/1 


of  + 
by  substituting  the  values: 

r 

R  =     I   RMf(x)*dx, 


-/ 

—    I   ^'(l),-/'^^2^/^         si 


The  preceding  applies  to  oscillators  without  condensers  in  series  but  is  easily 
modified  so  as  to  apply  to  oscillators  having  series  condensers. 

41  A.  BLONDEL,  Assoc.  franc,  pour  Pavancement  des  sciences.     Congres  d'Angers, 

1903. 

42  Elementary  treatment  of  the  action  of  capacities  and  inductive  coils  in  antennae, 

see,  e.g.,  A.  GUYAU,  Lum.  61.,  16,  13,  1911. 

43  Detailed  treatment  in  EMS,  p.  400  et  seq. 

44  Discussions  of  coefficients  of  self-induction  and  mutual  induction :  G.   GLAGE, 

Jahrb.,  2,  361  et  seq.,  501  et  seq.,  593  et  seq.,  1909,  and  particularly  E.  B.  ROSA 
and  F.  W.  GROVER,  Bullet.  Bur.  of  Standards,  8,  1  et  seq.,  1911. 

46  Articles  on  the  resistance,  self-induction  and  capacity  of  coils  of  solid  wire  and 
wire  braid:  (1)  Theoretical:  A.  SOMMERPELD,  Ann.  Phys.,  24,  609,  1907. 
J.  W.  NICHOLSON,  Jahrb.,  4,  26  et  seq.,  1910.  L.  COHEN,  Bull.  Bur.  of  Stand- 
ards, 4,  No.  76,  1907-1908.  W.  LENZ,  Ann.  Phys.,  37,  923,  1912.  H.  G. 
MOLLER,  Ann.  Phys.,  36,  738  et  seq.,  1911  (regarding  braided  wires).  Experi- 
mental: TH.  P.  BLACK,  Ann.  Phys.,  19,  157,  1906.  A.  MEissNER.23  A.  ESAU, 
reference  list  summarizing  his  articles:  Jahrb.,  4,  490  et  seq.,  1911.  R.  LINDE- 


412  WIRELESS  TELEGRAPHY 

MANN,  reference  list  of  articles:  Jahrb.,  4,  561  et  seq.,  1911.  K.  HERRMANN, 
Verb,  physik.  Ges.,  13,  978,  1911. 

46  Concerning  the  effective  resistance  of  wires  subjected  to  two  simultaneous  undamped, 

sinusoidal  and  damped,  non-sinusoidal  oscillations:  BRYLINSKI,  Bull,  de  la 
soc.  intern,  des  electriciens  (2),  6,  255,  1906. 

47  Rheostat,  for  rapid  oscillations,  of  wires  having  small  cross-section  and  low  conduc- 

tivity: C.  TISSOT,  Bull,  de  la  Soc.  intern,  des  electr.  (2),  6,  340,  1906.  W. 
HAHNEMANN,  Jahrb.,  2,  314,  1909. 

48  P.  BRENOT,  Lum.  el.,  15,  259  et  seq.,  1911. 

49  Resistance  and  current  distribution  in  rectangular  wire  (bands) :  W.  EDWARDS, 

El.,  68,  18,  1912  (theoretical).  J.  BETHENOD,  Jahrb.,  2,  379  et  seq.,  1909  (ex- 
perimental). 

50  N.  TESLA'S  researches  in  polyphase  currents,  etc.,  by  TH.  C.  MARTIN,  pp.  222,  314. 

(Halle,  1895.) 

51  Construction  of  C.  LORENZ  Co.  to  whose  courtesy  the  illustration  is  due. 

510  This  is  not  the  only  possibility.  For  instance,  the  same  image  would  be  produced 
if  the  discharge  frequency  and  the  revolutions  per  second  were  in  the  ratio 
3:4  or  5:4. 

52  E.  NESPER,  Jahrb.,  2,  92  et  seq.,  319  et  seq.,  3,  376  et  seq.,  1910. 

53  The  Rendahl  variometer  was  apparently  proposed  independently  by  PERI  (see 

ETZ,  32,  247,  1911). 

54  Thanks  are  due  to  the  DR.  E.  F.  HUTH,  G.  m.  b.  H.,  Berlin,  SO,  Erdmannshof,  for 

this  illustration. 

55  Thanks  are  due  to  DR.  L.  COHEN  (Nat.  Elec.  Sign.  Co.),  for  this  illustration. 

56  See  J.  MOSCICKI,  ETZ,  25,'  527,  1904.     C.  MULLER  (Ann.  Phys.,  28,  585  et  seq., 

1909)  also  proposed  a  good  form  of  jar. 

57  Compressed  air  (or  gas)  condensers,  proposed  by  T.  JERVIS-SMITH  (Nature,  48,  64, 

1893,  quoted  in  El.,  55,  912,  1905).     R.  FESSENDEN,  ETZ,  1905,  950.     M. 

WlEN.17 

In  regard  to  the  dielectric  strength  of  compressed  gases  see  M.  WOLF,  Wied. 
Ann.,  37,  306,  1889,  and  E.  A.  WATSON,  Journ.  Inst.  Elec.  Engs.,  40,  6,  1908. 
570  According  to  G.  W.  PIERCE, l  p.  114,  the  variable  condenser  was  proposed  by 
KORDA  as  early  as  1893. 

58  From  a  pamphlet  of  the  physikalisch-technischen  Laboratorium :  DR.  G.  SEIBT, 

Berlin-Schoneberg. 

59  From  Jahrb.,  4,  439,  1911. 

60  Construction  of  H.  BOAS  Co.  (Berlin). 

61  From  Jahrb.,  4,  229,  1911. 

62  See  P.  BRENOT,  Lum.  el.  (2),  11,  427,  1910. 

8V 

63  This,  of  course,  also  follows  directly  from  /  =  —  C  -rr- 

64  Gap  length  and  breakdown  potential:  A.  HEYDWEILLER,   Wied.  Ann.,  48,  235, 

1893.  S.  M.  KINTNER,  Proc.  Amer.  Inst.  El.  Engs.,  24,  523,  1905.  J.  A. 
FLEMING.1  More  recent  works  are:  J.  ALGERMissEN.65  E.  VOIGT,  Ann. 
Phys.,  12,  403,  1903.  C.  MuLLER56  (in  conjunction  with  MULLER,  see  M. 
TOEPLER,  Ann.  Phys.,  29,  153,  1909).  E.  HUPKA,  Ann.  Phys.,  36,  440  et  seq., 
1911.  W.  WEICKER,  ETZ,  32,  436  et  seq.,  460  et  seq.,  1911.  In  regard  to  prin- 
cipal points  in  measurement  of  gap  length  see  M.  TOEPLER,  Ann.  Phys.,  19, 
191,  1906;  ETZ,  28,  998  et  seq.,  1907. 

65  See  J.  ALGERMISSEN,  Diss.  Strassburg,  1906;  Ann.  Phys.,  19,  1016,  1906. 

66  E.  WARBURG,  Wied.  Ann.,  59,  1,  1896;  62,  385,  1897. 

67  If  V  is  the  potential  across  a  poor  insulator  of  resistance  R,  then  the  quantity  of 

electricity  which  is  lost  by  leakage  through  the  insulator  in  a  given  time,  t, 


BIBLIOGRAPHY  AND  NOTES  ON  THEORY  413 


is  equal  to  ^   I   I  V\  dt  (in  which  |  F|  is  the  absolute  value  of  F).     The  quantity 

lost,  therefore,  increases  as  the  duration  of  the  potential  increases. 
Concerning  insulating  materials  for  rapid  oscillations  see  S.  H.  HILLS,  EL,  65,  303, 
1910. 


Veff 

for  7  =  7 oe      T  .  sin  wt  and  d"^.  2-n-  [Art.  8c]. 


-         tf 

»-*( 

r"  i   ,\ 

70  For  one  discharge  we  have    I      Izdt  =  „,,.  •  702,  if  7  =  7o  ( 1  —  Tfi  t  }  sin  wt  and  a  ^  1 

[Art.  9a]. 

71  See  A.  WASMUS,  Diss.  Braunschweig,  1909.     ETZ,  31,  199,  1910. 

72  Jahrb.,  5,  517,  1911;  Jahrb.,  6,  28,  1913.     W.  STEINHAUS  Phys.  Zeitschr.,  12,  657, 

1911. 

73  A.  ESPINOSA  DE  LOS  MONTEROS,  Jahrb.,  1,  323,  1908. 

74  Articles  on  bolometers:  C.  TISSOT,  Ann.  Chim.  Phys.  (8),  7,  1906  or  separately: 

Etude  de  la  resonance  des  system es  d'antennes,  p.  20  et  seq.,  Paris,  1906. 
K.  E.  F.  SCHMIDT,  Phys.  Zeitschr.,  8,  601,  1907.  BELA  GATI,  EL,  58,  983,  1907; 
Jahrb.,  2,  109,  1908;  Phys.  Zeitschr.,  10,  322,  897,  1909.  J.  RAUTENKRANZ, 
Phys.  Zeitschr.,  10,  93,  1909.  H.  ZOLLICH,  Phys.  Zeitschr.,  10,  899,  1909. 
W.  KEMPE,  Phys.  Zeitschr.,  11,  331,  1910.  B.  S.  COHEN,  Journ.  Inst.  El. 
Engs.,  39,  503,  1907. 

75  Articles  on  thermocouples:  H.  BRANDES,  Phys.  Zeitschr.,  6,  503,  1905.     W.  VOLGE, 

ETZ,  1906,  467.  L.  W.  AUSTIN,  Phys.  Zeitschr.,  12,  1133,  1226,  1911.  C.  M. 
DOWSE,  EL,  65,  765,  1910. 

76  W.  DUDDELL,  Phil.  Mag.  (6),  8,  91,  1904;  Electrician,  55,  260,  1905. 

77  W.  GERLACH,  Phys.  Zeitschr.,  13,  589,  1912. 

78  A.  ESPINOSA  DE  LOS  MONTEROS,  Jahrb.,  1,  327,  1908. 

79  L.  W.  AUSTIN,  Bull.  Bur.  Stand,  7,  315,  1911;  Phys.  Zeitschr.,  12,  1133,  1911. 

According  to  the  latter  article,  the  "perikon"  detector  produced  a  deflection 
of  3  scale  divisions  in  a  2000  ohm  galvanometer  (1  scale  div.  =  1.28  X  10~9 
amp.),  for  a  MORSE  dash  when  the  tone  was  just  audible  in  the  most  sensitive 
telephones.  In  regard  to  a  magnetic  detector  for  measuring  purposes  see  R. 
ARNO,  Lum.  el.  (2),  6,  344,  1909. 

80  That  is, 

&n  =  -Lsl2,-jf;   8i2  =  -Ls2l  -^ 

The  differential  equations  for  two  circuits  carrying  quasi-stationary  current  and 
which  are  magnetically  coupled  are 

^  +  Ri^df  +Lid^  +Lsi2^J  =  ° 

ll  dl,  d*I2  d*I\  (1) 

If  the  circuits  have  pure  conductive  coupling, 

(2) 


414  WIRELESS  TELEGRAPHY 

in  which  Ri  and  Rz  are  the  total  resistances  of  th<e  primary  and  secondary  cir- 
cuits respectively,  R,  the  resistance  common  to  both  circuits. 
If  the  circuits  have  pure  electric  coupling, 


n 


(3) 


in  which  C\  and  Cz  are  the  total  effective  capacities  of  the  primary  and  secondary 
circuits  respectively,  C  the  capacity  common  to  both  circuits. 
If  the  current  is  not  quasi-stationary  in  either  of  the  two  circuits,  say  in  the 
secondary,  the  energy  equation  for  the  case  of  magnetic  coupling  is  found  as 
follows : 

Assume  that  the  current  amplitude  may  be  considered  as  uniform  along  the 
entire  coupling  (x  =  k)  in  the  secondary  circuit  as  well  as  the  primary.  Let 
Z/si2  and  L«2i  be  the  coefficients  of  mutual  induction  for  the  case  of  quasi- 
stationary  currents  in  both  circuits  and  let 

L12=L*12. /(*)[*=*]  1  (see  Note  40) 

L2l  =  Ls2l.f(x)[x  =  k]  j 

Then  the  energy  transferred  per  second  from  the  secondary  to  the  primary 
circuit  is  equal  to 

L      7i^ 

and  the  energy  transferred  per  second  from  the  primary  to  the  secondary  cir- 
cuit is 


The  differential  equations  therefore  take  the  form 

7l    4.  »   d/1  4.  T    <*2/1  4.  r     <*2I/21         n 

c'1  +  Ridr+Lidt^~  +  L^~dt^ 

N  d\I*\  d*\h\    .'dli      n 

~C,  +  Rz~dT  +  L2~dt^  +  L^dT 

(Symbols  Cz,  Rz  and  Lz  are  used  just  as  in  Note  29),  which  are  the  same  as  for 
magnetic  coupling  of  quasi-stationary  currents  (equation  1). 
If  two  different  oscillations  occur  in  each  circuit  [Art.  58],  it  must  not  be  for- 
gotten that  the  current  and  potential  distribution  [/(#)  and  <f>(x)]  and  therefore 
the  values  of  R,  C  and  L  are  different  for  the  two  oscillations  (A.  SLABY).  So 
far  as  the  author  knows  no  theory  (mathematical)  which  takes  this  fact  into 
account  has  been  worked  out  to  date  ;  however,  it  is  not  probable  that  the  results 
are  much  different  than  those  obtained  with  the  present  theory. 

81  J.  v.  GEITLER  (Wien.  Ber.,  104,  II,  169  et  seq.,  1895;  Wied.  Ann.,  55,  513,  1895) 

and  J.  ZENNECK,  Phys.  Zeitschr.,  4,  656,  1903. 

82  Thanks  are  due  to  the  TELEFUNKEN  Co.  of  Berlin  for  this  illustration. 

83  See  EMS,  634  et  seq. 

84  V.  BJERKNES,  Wied  Ann.,  44,  74,  1891;  55,  121,  1895. 

85  These  relations  hold  for  primary  circuits  containing  a  spark  gap  only  if  the  ampli- 

tude curve  is  an  exponential  curve. 

Nor  do  they  hold  in  the  case  di  =  dz  =  d.     In  this  case,  the  oscillation  in  the 

secondary  circuit  is  of  the  form  7  =  I§ie~ift   sin  ut. 

86  M.  WIEN,  Jahrb.,  1,  462,  1908;  Ann.  Phys.,  25,  625,  1908. 

87  This  is  true  only  if  there  is  no  quenching  action  [Art.  62  et  seq.]  and  even  if  this  is 


BIBLIOGRAPHY  AND  NOTES  ON  THEORY  415 

not  the  case,  the  amplitude  of  one  of  the  oscillations  can  be  zero.  Whether 
or  not  this  occurs  depends  upon  the  initial  conditions  (see  91). 

88  H.  DIESSELHORST,  Ber.  deutsch.  physik.  Ges.,  5,  320,  1907;  6,  306,  1908;  ETZ,  1908, 

703.  H.  RAU,  Jahrb.,  4,  52,  1910.  (RAU,  in  order  to  obtain  spark  photographs 
inserted  a  small  gap  in  the  secondary  circuit  also.) 

89  P.  DRUDE,  Ann.  Phys.,  13,  512  et  seq.,  1904.     For  the  theory  of  coupled  circuits 

also  see:  B.  MACKU,  Jahrb.,  3,  104  et  seq.,  329  et  seq.,  1910.  A.  KALAHNE, 
Jahrb.,  4,  357  et  seq.,  1911.  The  disadvantage  of  the  approximation  methods 
of  L.  COHEN  (Jahrb.,  2,  448  et  seq.,  1909)  and  J.  S.  STONE  (Lum.  61.,  12,  435, 
1910;  ETZ,  33,  111,  1911)  is  that  the  degree  of  accuracy  of  their  results  cannot 
be  predetermined. 

90  C.  FISCHER,  Ann.  Phys.,  22,  265,  1907.     M.  WIEN,  Phys.  Zeitschr.,  7,  871,  1906, 

8,  10  et  seq.,  1907;  ETZ,  1906,  839.  Also  see  J.  KAISER,  Phys.  Zeitschr.,  10, 
886,  1909.  C.  FISCHER,  Phys.  Zeitschr.,  11,  420,  1910.  W.  BIERLEIN,  Jahrb., 
6,  29,  1912.  E.  TALSCH,  Jahrb.,  6,  35,  1912. 

91  What  follows  holds  true  only  under  the  following  initial  conditions:  when  t  =  0 

7i  =  Vx0,  /i  =  0;  72  =  0;  h  =  0 

Under  other  conditions  in  fact  it  may  happen  that  only  one  oscillation  occurs. 
(A.  SLABY,  ETZ,  1904,  1086,  M.  WIEN,  ETZ,  1906,  837.)  The  relations  given 
in  a  and  b  are  easily  deduced  from  the  work  of  P.  DRUDE.  89  The  vector  dia- 
gram holds  for  the  beginning  (initial  conditions)  of  the  oscillations.  After- 
ward it  applies  only  to  currents  of  constant  frequency. 
910  J.  ZENNECK,  Phys.  Zeitschr.,  6,  198,  1905. 

92  M.  WIEN,  Jahrb.,  1,  469,  1908;  4,  135,  1911;  Ann.  Phys.,  25,  625,  1908;  Phys. 

Zeitschr.,  11,  76,  311,  1910. 

93  H.  BOAS,  Jahrb.,  5,  563,  1912. 

94  A.  ESPINOSAS  DE  LOS  MoNTEROS,  Jahrb.,  1,  480,  1908.     The  hydrogen  spark  gaps 

have  been  very  carefully  studied  by  B.  GLATZEL.  Summary  of  his  articles  in 
Jahrb.,  4,  400,  1911.  For  special  methods  of  connection  employing  two  or  more 
spark  gaps  in  series  see  Jahrb.,  5,  437,  1912;  EL,  68,  428  et  seq.,  1911. 

95  R.  RENDAHL,  Phys.  Zeitschr.,  9,  203,  1908.     B.  GLATZEL,  Ber.  der  deutschen  phy- 

sik. Ges.,  6,  54,  1908;  Jahrb.,  2,  65,  1908.     A.  ESPINOSA  DE  LOS  MoNTERos.94 
950  The  coupling,  however,  must  not  be  so  loose  that  the  duration  of  half  of  a  pulsa- 
tion occupies  considerable  time  during  which  the  oscillations  have  an  appreci- 
able amplitude.     For,  as  the  two  coupling  waves  exist  during  the  first  half 
pulsation,  the  object  of  the  quenched  gap  would  not  be  completely  secured. 

96  Regarding  the  relation  of  the  spark  frequency  to  the  effectiveness  of  the  quenching 

action,  see  H.  ROHMANN,  Phys.  Zeitschr.,  12,  649,  1911. 

97  B.  MACKU,  Ann.  Phys.,  34,  941,  1911. 

97aS.  SUBKIS,  Jahrb.,   5,  507,    545,    1912;    Diss.    Braunschweig,    1911.     Also  see 

C.  FISCHER.115 

98  G.    GLAGE,    Experimental    investigations   with    the    resonance    inductor.     Diss. 

Strassburg,  1907.  H.  BOAS,  Jahrb.,  3,  432,  607,  1910.  K.  ROTTGARDT,  Phys. 
Zeitschr.,  12,  652,  1911.  8.  KIMURA,  Jahrb.,  5,  222,  1911,  6,  459,  1912.  For 
the  theory,  see  G.  SEIBT,  ETZ,  1904,  276.  G.  BENISCHKE,  ETZ,  28,  2d  issue, 
1907.  J.  BETHENOD,  Jahrb.,  1,  534,  1908.  Historical:  P.  BRENOT,  Lum.  61. 
(2),  11,  167,  1910. 
99  Integral  of  the  equation  for  the  discharge  of  condenser  circuits 


in  the  case  of  aperiodic  discharge. 


416  WIRELESS  TELEGRAPHY 

100  Integral  of  the  differential  equation 

*  +  *£-'  - 

101  More  detailed  treatment  in  EMS,  Chap.  XIII  and  XIV. 

102  The  wave-length,  X,  obtained  in  this  way,  is  really  too  small  by  an  amount  AX, 

which  is  given  by 

AX       di(di+d2) 


X  87T2 

(B.  MACKLT,  Jahrb.,  2,  251,  1909).  In  regard  to  a  zero  method  for  determining 
the  frequency,  see  G.  SEIBT,  Jahrb.,  5,  407,  1912. 

103  E.  DORN,  Ann.  Phys.,  20,  127,  1906. 

104  See,  e.g.,  the  corresponding  paragraphs  in  F.  KOHLRAUSCH,  Lehrbuch  der  praktis- 

chen  Physik. 

105  Comparative  tests  by  different  methods:  H.  DIESSELHORST.*     Also  see  A.  CAMP- 

BELL, EL  64,  612  et  seq.,  1912. 

106  See,  e.g.,  EMS,  p.  711. 

107  More  accurate  discussion  of  the  resonance  method  and  the  necessary  corrections: 

B.  MACKu.102     Also  see  M.  K.  GROBER,  Phys.  Zeitschr.,  12,  121,  1911. 

108  H.  BRANDES,  Ann.  Phys.,  22,  645,   1907.     Graphic  method  by  F.  EGER,   Diss. 

Greifswald,  1908. 

109  L.  KANN,  Jahrb.,  4,  297,  1911;  Phys.  Zeitschr.,  11,  503,   1910.     The  BRANDES 

method  is  also  the  basis  of  an  arrangement  of  P.  LUDEWIG  (Phys.  Zeitschr., 
12,  763,  1911;  Jahrb.,  5,  390,  1912),  which  gives  a  direct  indication  of  the 
decrement. 

110  See  G.  JONAS,  Diss.  Strassburg,  1907. 

111  H.  RlEGGER.7 

112  B.  MACKtr,  Ann.  Phys.,  34,  941,  1911. 

113  M.  WiEN86  and  Phys.  Zeitschr.,  9,  537,  1908.     B.  MACKU102  and  Phys.  Zeitschr., 

9,  437,  646,  1908. 

114  S.  LOEWE,  Jahrb.,  6,  325,  1912. 

115  Concerning  the  POULSEN  arc  for  measuring  :  RAUSCH  VON  TRAUBENBERG  and  B. 

MONASCH,  Phys.  Zeitschr.,  8,  925,  1907;  9,  251,  1908.  C.  FISCHER,  Ann. 
Phys.,  28,  57,  1909;  32,  979,  1910.  F.  KIEBITZ,  Ber.  physik.  Ges.,  12,  99,  1910; 
Jahrb.  ,2,  357  et  seq.,  1909.  PHYS.  TECHN.  REICHSANSTALT:  Zeitschr.  f.  Instru- 
mentenkunde,  28,  148,  1908.  R.  LINDEMANN,  Ber.  physik.  Ges.,  11,  28,  1909. 
K.  VOLLMER,  Jahrb.,  3,  123,  1909.  According  to  G.  SZIVESSY  (Jahrb.,  3,  250 
et  seq.,  1910)  an  arc  in  bisulphide  of  carbon  vapor  gives  very  steady  oscillations. 

116  In  regard  to  precautions  for  the  use  of  these  spark  gaps  for  measuring  purposes,  see 

S.  LOEWE.  114 

117  H.  TH.  SIMON,  Phys.  Zeitschr.,  4,  737,  1903.     G.  W.  PIERCE,  Phys.  Zeitschr.,  6, 

426,  1904. 

118  W.  EICKHOFF,  Phys.  Zeitschr.   8,  923,  1907.     According  to  W.  F.  ZORNIS  the  point 

on  copper  electrodes  causes  an  increase  in  the  spark  damping.  J.  A.  FLEMING 
and  H.  W.  RICHARDSON  (EL,  63,  175,  1909)  recommend  air  blowers  to  make  the 
discharges  more  regular.  This  result,  however,  is  not  always  accomplished 
(i.e.,  with  all  types  of  gaps)  by  a  blower. 

119  Another  procedure  is  to  make  the  coupling  looser  gradually  until  the  value,  which 

is  obtained  from  the  resonance  curve  in  accordance  with  Art.  74  remains  con- 
stant. The  theoretical  requirement  for  this  condition  is:  ir2K2  <^cW2.86 
Also  see  R.  LINDEMANN'S  115  method. 

120  M.    WIEN,    Phys.  Zeitschr.,  8,  764,  1907:  with  di  =  0.11,  d*  =  0.015  and  K  = 

0.014  the  error  becomes  30  per  cent. 


BIBLIOGRAPHY  AND  NOTES  ON  THEORY  417 

121  Complete  treatment  in  the  book,  Die  Frequenzmesser  und  Dampfungsmesser  der 

Strahlentelegraphie,  by  E.  NESPER,  Leipzig,  1907. 

122  E.g.,  EL,  68,  249  et  seq.,  1911. 

123  THOR.  G.  THORNBLAD,  Jahrb.,  4,  97  et  seq.,  109  et  seq.,  217  et  seq.,  1911. 

124  E.  NESPER,  Jahrb.,  1,  112,  1907. 

125  J.  A.  FLEMING,  EL,  58,  495  et  seq.,  536  et  seq.,  1907. 

126  Lum.  el.,  9,  391,  1910. 

127  Ann.  Phys.,  8,  211,  1902. 

128  R.  HIRSCH,  Jahrb.,  4,  250,  1911. 

129  L.  MANDLESTAM  and  N.  PAPALEXI,  Jahrb.,  4,  605,  1911.     The  high  degree  of  ac- 

curacy of  the  method  for  determining  frequency  is  well  shown  in  the  article 
by  H.  ROHMANN,  Diss.  Strassburg,  1911;  Ann.  Phys.,  34,  979,  1912. 


130  The  dynamometer  effect  is  =  y  I  IJ2dt 

131  Another  method  for  determining  the  dynamometer  effect  by  means  of  a  differen- 

tial air  thermometer  by  L.  KANN109  and  L.  ISAKOW,  Phys.  Zeitschr.,  12,  1224, 
1911. 

132  The  e.m.f.  induced  in  the  ring  is  displaced  90°  with  respect  to  7'2,  and  73  is  in  turn 

displaced  90°  from  this  e.m.f. 

133  On  the  assumption  that  the  current  curve  is  the  same  in  both  cases  [see  Art.  lie,  2]. 

134  W.  EICKHOFP,  Phys.  Zeitschr.,  8,  564,  1907.     A.  JOLLOS  (Diss.  Strassburg,  1907) 

was  probably  the  first  to  show  that  an  unsymmetrical  resonance  curve  was  the 
result  of  condenser  brush  discharge.  Concerning  the  brush  discharge  of  con- 
densers also  see  M.  WiEN17  and  L.  W.  AusTiN.21 

135  From  C.  FiscHER.90 

136  This  method  was  developed  at  the  suggestion  of  the  author  by  C.  FISCHER,  Ann. 

Phys.,  19,  182,  1906. 

137  The  use  of  damping  meter  of  P.  LUDEWIG  for  determining  the  degree  of  coupling 

(Phys.  Zeitschr.,  13,  450,  1912)  is  also  based  upon  this  relation. 

138  B.  MACKU,  Jahrb.,  3,  580  et  seq.,  1910. 

139  TELEFUNKEN  Co.,  EL,  68,  171,  1911. 

140  Experiments  at  the  physik.  Inst.  Danzig-Langfuhr. 

141  Spark  photographs  can  also  be  used  instead  of  the  resonance  curves.     H.  RAU.SS 

142  R.  A.  FESSENDEN,  ETZ,  1906,  690. 

143  Antennae  with  increased  end  capacity  were  one  of  the  first  forms  of  antennae  used 

by  MARCONI  and  LODGE.     Their  fundamental  advantages  are  given  by  A. 

BLONDEL.41 

144  Additional  details  regarding  the  TELEFUNKEN  Go's  antennae:  SIEWERT,    ETZ, 

1906,  965.  R  SOLFF,  ETZ,  1906,  p.  875  et  seq.  COUNT  ARCO,  A.  E.  G.  lec- 
tures, lecture  of  Dec.  9,  1911.  H.  BREDOW,  Jahrb.  der  Schiffbau-technischen 
Ges.,  1912,  105  et  seq.  Various  articles  in  the  TELEFUNKENZEITUNG. 

145  O.  LODGE  and  A.  MUIRHEAD,  EL,  51,  1036,  1903.     See  EL,  62,  170,  1908. 

146  COUNT  ARCO.144 

147  L.  W.  AUSTIN,  Bullet.  Bur.  Stands,  7,  315  et  seq.,  1911. 

148  Various  constructions  for  masts:  Jahrb.,  3,  203,  521,  1910;  4,  309,  652,  1911.     EL, 

68,  213,  1911. 

149  O.  LODGE  and  A.  MUIRHEAD  at  times  erected  their  counterpoise  several  meters 

above  the  ground  (see  Jahrb.,  3,  1,  1909). 

150  W.  BURSTYN,  ETZ,  1906,  1117.     F.  KIEBITZ,  Ann.  Phys.,  32,  961,   1910.     M. 

REICH,  Phys.  Zeitschr.,  13,  228  et  seq.,  1912;  Jahrb.,  6,  176  et  seq.,  253  et  seq., 
1911.     H.  TRUE,  Jahrb.,  5,  125  et  seq.,  1911.     P.  BARRECA,  Jahrb.,  6,  285  et 
seq.,  1912. 
27 


418  WIRELESS  TELEGRAPHY 

151  Regarding  radio-apparatus  for  airships  and  tests  therewith  see  Jahrb.,  3,  315,  434, 

1910,  4,  227,  1911,  6,  70,  1912.  FERRIE,  Lum.  el.  12,  99  et  seq.,  1910.  TELE- 
FUNKENZEITUNG,  1,  66,  1911.  K.  SOLFF,  Jahrb.,  3,  392  et  seq.,  1910.  K. 
LUBOWSKY,  ETZ,  32,  1265,  1911.  M.  DIECKMANN,  Jahrb.,  6,  51,  1912. 
"Luftfahrt  und  Wissenschaf t "  No.  2,  1912.  P.  LUDEWIG,  Jahrb.,  6,  10,  1912. 
H.  MOSLER,  Jahrb.,  6,  44,  1912. 

152  Regarding  oscillations  induced  in  all  metal  parts  near  quenched  gap  circuits,  see 

5.  LOEWE.114 

153  According  to  DR.  MEISSNER,  however,  the  dangerous  effect  upon  the  ropes  and  the 

bag  of  the  balloon  is  greatly  increased  when  large  current  effect  is  used. 

154  Tests  of  the  accuracy  of  the  methods  given  in  Art.  97 :  A.  ESAU,  Phys.   Zeitschr. 

13,  658,  1912. 

155  C.  FISCHER,  Ann.  Phys.,  32,  979  et  seq.,  1910. 

156  Concerning  the  increase  in  antenna  capacity  due  to  ice,  rain,  snow,  etc.,  and  the 

relation  between  antenna  damping  and  weather  conditions  see  A.  ESAU, 
Phys.  Zeitschr.,  13,  721,  1912. 

157  COUNT  ARCO,  ETZ,  1910,  508. 

158  See,  e.g.,  B.  C.  TissoT,74  p.  139,  148  et  seq. 

169  Regarding  antenna  insulators  used  by  the  TELEFUNKEN  Co.,  see  H.  BREDOW.144 
For  methods  of  reducing  brush  discharge  see  Jahrb.,  4,  441,  1911.  H.  LANGE, 
Jahrb.,  4,  442,  1911. 

160  COUNT  ARCO,  Jahrb.,  2,  551  et  seq.,  1909. 

161  Regarding  total  antenna  resistance  and  its  determination,  see  C.  FISCHER,  Phys. 

Zeitschr.,  12,  295,  1911.     L.  W.  AUSTIN,  Phys.  Zeitschr.,  12,  924,  1911;  Jahrb., 

6,  574  et  seq.,  1912.     There  seems  to  be  a  relation  between  the  total  antenna 
resistance  and  the  wave-length  of  the  oscillation,  such  that  the  total  resistance 
first  decreases  and  then  again  increases  in  a  straight  line  (uniformly)  as  the 
wave-length  is  increased.     The  decrease  at  first  is  probably  due  to  the  decrease 
in  R%  accompanying  the  increase  in  wave-length,  the  subsequent  increase  in 
total  resistance  must  be  due  to  an  increase  in  the  resistance  of  the  earth,  at  any 
rate  it  varies  with  the  amount  of  moisture  in  the  ground. 

162  J.  ERSKINE-MURRAY,  Jahrb.,  6,  499,  1912.     M.  REICH,  Phys.  Zeitschr.,  13,  228 

et  seq.,  1912. 

163  8  =    I     Exdx,  where  dx  is  an  element  of  the  antenna,  Ex  the  component  of  the 

electric  field  strength  along  this  element  and  h  the  length  of  the  antenna. 

164  Bullet.  Soc.  d'encouragement  p.  Pindustrie  rationale,  3,  1632,  1898. 

165  F.  BRAUN,  D.R.P.  No.  109378  (1899),  Electrician,  62,  19,  1904;  Phys.  Zeitschr., 

6,  193,  1904. 

166  L'Electricien,  42,  107,  1911. 

167  Literature  of  compressed  air  spark  gaps,  F.  JERVIS-SMITH,  EL,  63,  720,  1909. 

168  G.  EICHHORN,  D.R.P.,  157056  (1903).     The  modification  (Fig.  218)  of  his  orig- 

inal arrangement  is  due  to  P.  PICHON  (TELEFUNKEN  Co.). 

169  B.  GLATZEL,  Phys.  Zeitschr.,  11,  893,  1910. 

170  S.  EISENSTEIN,  EL,  65,  848,  1910. 

1700  R.  C.  GALLETTI  (EL,  66,  570,  1911;  ETZ,  32,  597,  1911,  D.R.P.,  245358). 

171  Other  methods  of  connection  by  G.  SEIBT,  D.R.P.,  241114  (1909).     B.  MACKU, 

EL,  68,  429,  1911. 

172  Jahrb.,  2,  229,  1909. 

173  COUNT  ARCO,160  B.  GLATZEL,  Jahrb.,  2,  90,  1908. 

174  A  two  plate  spark  gap  was  probably  first  proposed  by  T.  B.  KINRAIDE,  U.  S.  Patent 

623316  (1898),  D.R.P.,  108924  (1899). 


BIBLIOGRAPHY  AND  NOTES  ON  THEORY  419 

175  EL,  63,  174  et  seq.,  374  et  seq.,  1909;  64,  153  et  seq.,  1909.     Tests  made  by  W.  H. 

ECCLES  and  A.  J.  MACKAWER,  EL,  64,  386,  1909;  Jahrb.,  4,  294,  1911. 

176  COUNT  ARCo,160  Jahrb.,  4,  79  et  seq.,  1910,  ETZ,  31,  506  et  seq.,  1910. 

177  O.  SCHELLER,  Jahrb.,  5,  243,  1911. 

178  W.  PEUCKERT,  Jahrb.,  3,  199,  1909.     A.  WASMUS.™    L.  H.  WALTER,  EL,  64,  550 

1910. 

179  Regarding  other  stations  of  the  TELEFUNKEN  Co.,  see  COUNT  ARCO,  176  H.  BREDow.144 

180  F.  G.  LORING,  EL,  67,  27,  1911. 

181  H.  RAU.88 

182  See  C.  MtiLLER56  and  then  also  M.  ToEPLER.64 

183  Such  meters  were  built,  though  for  quite  other  purposes,  by  Siemens  and  Halske, 

Berlin,  at  the  suggestion  of  the  author. 

184  See,  e.g.,  G.  BRION,  Leitfaden  zum  elektrotechnischen  Praktikum,  p.  102  (B.  G. 

TEUBNER,  1910).  The  Dolezaleck  electrometer  can  also  be  used  for  power 
measurements;  e.g.,  see  M.  REICH.  15° 

185  W.  BURSTYN,  Jahrb.,  6,  217,  1912,  proposes  methods  for  making  and  breaking  the 

circuit  of  the  field  excitation  current. 

186  See  P.  O.  PEDERSEN,  Jahrb.,  4,  524,  1911.     Regarding  the  high-speed  telegraph 

apparatus  used  by  POULSEN,  see  ETZ,  32,  1164,  1911. 

187  EL,  60,  546,  883,   1908.     Other  spark  gaps  having  smooth  rotating  electrodes: 

S.  EISENSTEIN,  Jahrb.,  5,  245,  1911.     W.  BURSTYN,  Jahrb.,  6,  212,  1912. 

188  L'Electricien,  42,  107,  1911. 

189  EL,  65,  847,  1910.     A  similar  arrangement  by  G.  FERRIE,  EL,  65,  135,  1910. 

190  EL,  64,  512  et  seq.,  1910.     This  gap  is  used  by  the  Soc.  franc,  radioelectrique. 

191  G.  MARCONI,  EL,  67,  532,  1911;  EL  World,  59,  887,  1912;  Jahrb.,  6,  438,  1913;  also 

see  E.  NESPER,  Helios,  18,  429,  1912.  As  MARCONI  employs  relatively  loose 
coupling  (5  per  cent.),  the  duration  of  half  a  pulsation  and  hence  of  the  time 
during  which  there  are  two  coupling  waves  present  in  the  antenna,  is  rather 
long.  Consequently  they  are  evident  in  the  resonance  curve.  See95a  and 
Art.  90a. 

192  See,  e.g.,  C.  C.  F.  MONCKTON,  EL,  56,  514,  1906. 

193  W.  H.  ECCLES  and  A.  J.  MACKOWER  (Jahrb.,  4,  253,  1911;  EL,  65,  1014,  1910)  find 

a  considerably  lower  efficiency  from  their  measurements,  which  latter,  however, 
are  open  to  criticism. 

194  W.  DUDDELL,  Phil.  Mag.  (6),  9,  299,  1905;  Proc.  Royal  Inst.,  May  17,  1912.     Also 

see  Jahrb.,  4,  202,  1911. 

195  E.  F.  W.  ALEXANDERSON,  Trans.  Amer.  Inst.  EL  Eng.,  28,  I,  399  et  seq.,  1910. 

196  R.  A.  FESSENDEN,  D.  R.  P.,  228,365,  1908. 

197  R.  GOLDSCHMIDT,  ETZ,  32,  54,  1911;  Jahrb.,  4,  341  et  seq.,  1911. 

198  we  may  either  conceive  the  alternating  field  of  frequency  JV'  as  made  up  of  two 

rotating  fields  of  opposite  direction  or  we  may  proceed  on  the  basis  that  the 
magnetic  flux  passing  through  R  must  be  of  the  form 

A  sin  (2irN  .  t  +  «)  cos  (2irNf  .  t  +  «') 
sin  [2w(N  +  N')t  +  (a  +  «')]  +  sin  [27r(AT  -  N')t  +  (a  -  «')] 


For  the  theory  of  the  GOLDSCHMIDT  machine  see  E.  RUSCH,  Jahrb.,  4,  348  et 
seq.,  1911.  B.  MACKU,  Jahrb.,  5,  5,  1911.  See  Note.  344 

1980  In  the  commercial  form,  condensers  d  and  C3  are  omitted. 

199  Very  little  has  so  far  been  published  regarding  the  new  high  frequency  generator  of 
COUNT  ARCO,  which  was  exhibited  at  the  international  convention  in  London 
in  1912.  See  Jahrb.,  5,  529,  1912.  TELEFUNKENZEITUNG,  Vol.  2,  No.  7,  p.  18. 
In  regard  to  the  generation  of  undamped  oscillations  by  means  of  a  series  ma- 


420  WIRELESS  TELEGRAPHY 

chine  with  a  condenser  connected  in  parallel  see  F.  FITZGERALD  (Eclair.  e"l., 
18,  386,  1892).  O.  M.  CORBINO  (Phys.  Zeitschr.,  8,  924,  1907;  9,  195,  704, 
1908;  Electrician,  61,  56,  1908).  R.  RUDENBERG  (Phys.  Zeitschr.,  8,  668, 
1907;  9,  556,  1908).  H.  BARKHAUSEN,  Das  Problem  der  Schwingungser- 
zeugung.  Diss.  Gottingen,  1907,  p.  37.  It  is  impossible  to  conclude  from  the 
results  obtained  to  date  whether  it  will  ever  be  possible  to  produce  undamped 
oscillations  for  wireless  telegraphy  by  this  method  in  a  practical  and  useful  way. 

200  EL.  THOMSON,  U.  S.  Pat.,  July  18,  1892  (quoted  in  EL  Review,  60,  328,  1907) ;  U.  S. 

Pat.  No.  500630,  July  4,  1893.  N.  TESLA  in  MARTIN'S  "Nichola  Teslas 
Untersuchungen  iiber  Mehrphasenstrome."  Halle,  1895.  FESSENDEN  claims 
to  have  made  his  first  attempts  in  this  direction  in  1899. 

201  W.  DUDDELL,  Electrician,  46,  269,  310,  1900. 

202  J.  WERTHEIM-SALOMONSON,  Electrician,  52,  126,  1904.     Eclairage  electr.,  38,  144, 

1904.     N  =  400,000  eye.  per  sec. 

203  V.  POULSEN,  Danish  Pat.  5590  (Sept.  9,  1902),  D.R.P.  162945  (July  12,  1903). 

204  por  further  details  see  the  TELEFUNKEN  Co.'s  pamphlet  describing  their  standard 

radio-telephone  station.  C.  SCHAPIRA  on  the  efficiency  of  the  high  frequency 
arc  lamp  with  subdivided  arc.  Diss.  Charlottenburg,  1908  and  Jahrb.,  2, 
54  et  seq.,  1908. 

205  P.  BRENOT  states  in  Lum.  41.  (2),  11,  170,  1910  (also  see  Lum.  el.  (2),  11,  197,  1910) 

that  A.  BLONDEL  employs  two  plates  in  petroleum  as  electrodes  and  impresses 
about  2000  volts  across  the  arc.  It  is  claimed  that  this  gives  greater  regularity 
than  the  POULSEN  method  but  does  not  secure  high  frequencies  so  easily.  The 
author  does  not  know  whether  the  BLONDEL  method,  which  is  very  similar 
to  the  PEUCKERT  method,  has  ever  been  used  in  practice. 

According  to  Jahrb.,  4,  522,  1911,  F.  JACOVIELLO  employs  metallic  electrodes, 
potentials  of  40,000  to  80,000  volts  and  impinges  a  stream  of  gas  upon  the  arc, 
approximately  in  the  direction  of  the  length  of  the  arc.  Whether  a  quenched 
gap  or  undamped  oscillations  were  used  is  not  clear  from  what  has  been 
published. 

206  From  W.  DUDDELL,  Proc.  Royal  Inst.,  May  17,  1912. 

207  Jahrb.,  1,  307,  1908. 

208  Data  on  POULSEN  stations: 

a.  LYNGBY  and  CULLERCOATS,  Jahrb.,  1,  154  et  seq.,  1907;  Electrician,  60,  355 

et  seq.,  1907. 
6.  KNOCKROE,  Jahrb.,  1,  430,  1908;  ETZ,  1908,  15. 

209  According  to  the  C.  LORENZ  Co.,  this  method  of  connection  originated  with  W. 

HAHNEMANN  and  O.  SCHELLER. 

210  P.  O.  PEDERSEN,  EL,  60,  547,  1908.     C.  LORENZ,  Jahrb.,  4,  333,  1911. 

211  H.  REIN,  Jahrb.,  4, 196, 1911  and  "Der  radiotelegraphische  Gleichstromtonsender," 

Langensalza,  1912. 

212  A  large  number  of  investigations  of  these  phenomena  have  been  made  during  recent 

years,  the  principal  ones  being  the  following : 

a.  O.  M    CORBINO,  Atti.  Assoc.  Elettrotecnica  Ital.,  Oct.,  1903  (mentioned  in 

Phys.  Zeitschr.,  9,  197,  1908). 
6.  A.  BLONDEL,  Eel.  El.,  44,  41  et  seq.,  81  et  seq.,  1905.     BLONDEL  was  the  first 

to  distinguish  the  different  kinds  of  oscillations. 

c.  H.  BARKHAUSEN,  Jahrb.,  1,  234  et  seq.,  1907. 

d.  H.  TH.  SIMON:  Various  articles,  in  part  jointly  with  M.  REICH.     The  articles 
are  quoted  in  the  general  discussion  by  H.  TH.  SIMON  in  Jahrb.,  1,  16,  1907. 

e.  W.  DUDDELL,  Electrician,  46,  268,  310,  1900. 

/.    G.  GRANQVIST,  Nov.  Act.  Reg.  Soc.  Scient.  Upsaliensis  (4),  1,  No.  5. 
g.  E.  RIECKE,  Gottinger  Nachr.  Math.-phys.  Kl.,  1907,  253. 


BIBLIOGRAPHY  AND  NOTES  ON  THEORY  421 

h.  K.  H.  WAGNER,   "Der  Lichtbogen  als  Wechselstromerzeuger."     Leipzig, 
1910. 

1.  For  a  comprehensive  survey  of  this  subject  see  H.  BARKHAUSEN,  "Das 
Problem   der   Schwingungserzeugung."     Diss.    Gottingen,    1907.     In  that 
article  one  question,  namely,  under  what  conditions  the  various  kinds  of 
oscillations  are  stable,  which  has  not  been  considered  in  this  book,  is  dis- 
cussed  in  detail.     In   other   respects   the   treatment   of   this  subject   in 
what  follows,  is  very  similar  to  that  given  by  BARKHAUSEN. 

213  This  is  really  a  portion  of  a  sine  curve.     See,  e.g.,  EMS,  p.  547. 

214  The  charging  curve  is  determined  by  the  equation 

V  =  70|_1  -e     S^J 
in  which  VQ  =  dynamo  voltage,  C  =  capacity  of  condenser. 

215  G.  W.  NASMYTH  (Jahrb.,  5,  269  et  seq.,  367  et  seq.,  1912)  has  given  formulae  for  the 

frequency  of  oscillations  generated  by  the  arc  method.  These  formulae  how- 
ever have  been  discussed  by  K.  VOLLMERIIS  and  P.  O.  PEDERSEN  (Jahrb.,  6, 
496,  1912). 

216  Regarding  the  function  of  the  magnetic  blowout  see  H.  RAUSCH  VON  TRAUBENBERG, 

ETZ,  28,  559,  1907.  H.  TH.  SIMON, 208  p.  65.  H.  BARKHAUSEN,208  p.  256.  K. 
.BIRKELAND  (Jahrb.,  2,  137,  1908)  suggests  a  radial  magnetic  field  for  producing 
a  rotating  arc. 

217  See  H.  BARKHAUSEN,  Jahrb.,  2,  40,  1909. 

218  In  Arts.  138,  139,  140  and  142  it  is  assumed  that  (1)  the  oscillations  are  undamped, 

(2)  the  atmosphere  is  an  absolute  non-conductor;  furthermore  in  Arts.  138  to 
140  it  is  taken  for  granted  that  the  assumed  conductivity  holds  for  the  entire 
portion  of  the  earth  which  comes  into  consideration.  As  to  the  first  assump- 
tion, L.  W.  AUSTIN  (Jahrb.,  6,  524,  1912)  was  unable  to  find  any  difference 
between  undamped  waves  and  waves  having  a  decrement  of  0.15  at  a  distance 
of  30  miles. 

219  As  early  as  1898,  A.  BLONDEL  (Compt.  rend.   Assoc.  franc..  Avancement    des 

sciences.  Congres  de  Nantes,  1898,  p.  212  et  seq.)  pointed  out  in  conjunction 
with  a  remark  of  POINCARE  that  the  action  of  the  earth  in  a  grounded  transmit- 
ter could  be  replaced  by  that  of  an  image  of  the  transmitter,  i.e.,  that  a  grounded 
transmitter  can  properly  be  conceived  as  one-half  of  a  HERTZ  lineal  oscillator. 

220  A  comparison  of  the  two  limiting  cases,  the  lineal  transmitter  (Figs.  27-30)  on  one 

hand  with  transmitter  having  uniform  current  amplitude  throughout,  as 
shown  for  example  in  EMS,  Figs.  613-621. 

221  J.  ZENNECK  (Ann.  Phys.,  23,  846,   1907).     Previous  to  this,  K.  ULLER  (Diss. 

Rostock,  1903)  had  already  investigated  the  action  of  the  waves  under  the 
assumption  that  they  are  entirely  surface  waves  and  that  the  earth's  surface 
possesses  a  high  degree  of  conductivity. 

222  A.  SOMMERFELD,  Ann.  Phys.,  28,  665,  1909;  Jahrb.,  4,  158,  1910. 

223  Regarding  the  conductivity  of  sea  water,  earths  and  rocks,  see  H.  SCHMIDT,  Jahrb., 

4,  636  et  seq.,  1911.  K.  ULLER,  Jahrb.,  4,  638,  1911.  H.  LOEWY,  Ann.  Phys., 
36,  125  et  seq.,  1911  and  discussion  thereof  by  J.  A.  FLEMING,  Jahrb.,  5,  515, 
1912. 

224  This  conception  that  the  waves  of  radio-telegraphy  are  of  the  nature  of  surface 

waves  was  probably  first  presented  by  A.  BLONDEL219  and  by  E.  LECHER 
(Phys.  Zeitschr.,  3,  273,  1901-1902).  Also  see  K.  ULLER,  "Die  Mitwirkung 
der'Erde  und  die  Bedeutung  der  Erdung  in  der  drahtlosen  Telegraphic,  Jahrb., 

2,  8,  1908. 

225  P.  EPSTEIN,  Jahrb.,  4,  176  et  seq.,  1910. 


422  WIRELESS  TELEGRAPHY 

226  H.  POINCARE,  Jahrb.,  3,  445,  1910.     J.  W.  NICHOLSON,  Review  of  his  articles, 

Jahrb.,  4,  20,  1910;  Phil.  Mag.,  21,  281,  1911.  H.  W.  MARCH  (Ann.  Phys.,  37, 
29,  1912.  Note  corrections  in  subsequent  issue  of  Ann.  Phys.).  H.  MAC- 
DONALD,  Phys.  Zeitschr.,  10,  771,  1909. 

227  H.  B.  JACKSON,  Proc.  Royal  Soc.,  70,  254  et  seq.,  1902. 

228  W.  DUDDELL  and  J.  E.  TAYLOR,  Electrician,  55,  260,  1905.     C.  TISSOT,  Electri- 

cian, 56,  848,  1906. 

229  F.  HACK,  Ann.  Phys.,  27,  43,  1908.     The  assumptions  are  the  same  as  in.221 

230  Electrician,  55,  409,  1905. 

231  F.  KIEBITZ,  Verh.  physik.  Ges.,  13,  876  et  seq.,  1911. 

232  A  reflection  of  this  kind  has  been  demonstrated  in  laboratory  experiments  with 

very  short  waves:  F.  ERB,  Diss.  Braunschweig,  1912.  Data  on  observations 
in  practice:  P.  SCHWARZHAUPT,  ETZ,  31,  113,  1911. 

233  See  L.  ZEHNDER,  ETZ,  32,  1101,  1911. 

234  In  regard  to  the  influence  of  the  weather  upon  the  antenna  oscillations  see  A. 

EsAU,156  O.  GULDENPFENNIG,  Jahrb.,  5,  73,  1911.  WILDMANN  (see  ERSKINE- 
MuRRAY1)  made  systematic  observations  for  over  a  year  on  the  effect  of  the 
weather  upon  the  communication  between  two  stations. 

235  H.  EBERT  (Jahrb.,  4,  160,  1911)  found  the  conductivity  of  the  air  at  a  height  of 

2500  m.,  in  bright  sunlight  and  in  a  downward  current  of  air,  to  be  twenty- 
three  times  as  great  as  the  conductivity  just  over  the  earth's  surface.  Re- 
garding the  effect  of  meteorological  conditions  upon  the  ionization  of  the 
atmosphere  see  K.  FISCHER,  ETZ,  32,  339,  1911. 

236  Jahrb.,  5,  532,  1911. 

236a  A.  BLONDEL41  was  probably  the  first  to  indicate  that  these  upper  strata  might  play 
an  important  part  in  determining  wave  propagation  (see,  e.g.,  B.  J.  ERKSINE- 
MuRRAY1).  This  view  is  based  on  the  assumption  of  a  very  good  conductivity 
for  the  upper  layers  of  the  atmosphere.  There  is  no  justification  for  supporting 
this  assumption  by  reference  to  conditions  in  the  GEISSLER  tube  or  in  J.  J. 
THOMSON'S  current  loop  without  electrodes,  for  in  both  these  cases  the  gas  is 
ionized  by  a  very  strong  electric  field,  which  does  not  exist  in  the  upper  atmos- 
pheric strata  in  wireless  telegraphy. 

237  J.  A.  FLEMING,  The  Marconigraph,  2,  179,  1912.     G.  W.  PIERCE,*  p.  139  states 

that  A.  E.  KENNELLY  has  shown  the  effect  of  day  and  night  to  be  due  to  a 
change  in  the  wave  front. 

238  According  to  DR.  A.  MEISSNER,  heavy  winds  of  long  duration,  which  tend  to  eradi- 

cate existing  heterogeneity  in  the  atmosphere,  increase  the  distance  effect. 
LEE  DE  FOREST  (Jahrb.,  6,  167,  1912)  reports  a  very  remarkable  observation 
of  interference  due  to  heterogeneity. 

239  G.  MARCONI,  EL,  49,  521,  1902;  54,  824,  1905. 

240  See  Jahrb.,  5,  621,  1912;  6,  151,  154,  1912.     A.  TURPAIN,  C.  R.,  154,  1457,  1912. 

W.  H.  ECCLES,  EL,  69,  109,  1912.  J.  A.  FLEMING,  EL,  69,  190,  1912;  TELE- 
FUNKENZEITUNG,  1,  89,  1912.  So  many  observers  have  failed  to  find  any  effect 
due  to  solar  eclipses  and  others  have  found  so  slight  an  effect,  that  it  may  be 
concluded  that  this  effect  is  hardly  greater  than  the  extent  of  the  errors  involved 
in  these  measurements. 

241  G.  MARCONI,  EL,  64,  379,  1909.     H.  J.  ROUND  had  already  (EL,  56,  714,  1906) 

stated  that  the  difference  between  day  and  night  range  is  much  greater  with 
short-  than  with  long  waves. 
842  Tests  made  at  the  Braunschweig  physik.  Inst.,  1907. 

243  For  tests  on  damping  of  antennse  in  daylight  and  at  night  see  note234;  also  H. 

MOSLER,  ETZ,  30,  301,  1909  and  P.  SCHWARZHAUPT,  ETZ,  32,  1313,  1912. 

244  L.  W.  AUSTIN,  Jahrb.,  5,  75,  1911;  Bull.  Bur.  Stands.,  7,  315  et  seq.,  1911. 


BIBLIOGRAPHY  AND  NOTES  ON  THEORY  423 

245  L.  W.  AUSTIN,  Jahrb.,  6,  417,  1912. 
2«  K.  SOLFF,  ETZ.,  1906,  896. 

247  J.  A.  FLEMING/  J.  ERSKiNE-MuRBAY1  and  G.  W.  PiEBCE1  give  general  and  in 

some  cases  more  complete  presentations  of  this  subject.  Also  see  S.  SACHS, 
Jahrb.,  1,  130,  279,  434,  584,  1908.  E.  NESPER,  Jahrb.,  4,  312,  423,  534,  1911. 

248  C.  TISSOT,  Electrician,  56,  848,  1906;  Industrie  electrique,  14,  161,  1906;  Journal 

de  Physique,  6,  279,  1907. 

249  G.  MARCONI,  Proc.  Royal  Soc.,  77,  413,  1906;  Electrician,  57,  100,  1906. 

250  Regarding  thermal  detectors:  W.   H.   ECCLES,   El.,   60,  587,   1908.     C.   TISSOT, 

Jahrb.,  2,  115  et  seq.,  1908.  E.  NESPER247,  references  in  Jahrb.,  3,  370,  430 
(1910);  4,  232  et  seq.  (1911).  On  thermal  detectors  with  a  rotating  electrode, 
see  El.,  62,  211,  1908  (L.  W.  AUSTIN);  Jahrb.,  2,  144,  1908  (TELEFUNKEN). 

251  Review   of  various   magnetic  wave  indicators  not   covered  by  note247:   L.    H. 

WALTER,  Electrician,  55,  83,  1905.  For  explanation  of  their  action  see  L.  H. 
WALTER  and  E.  MADELUNG,  Ann.  Phys.,  17,  861,  1905;  W.  H.  ECCLES,  Elec- 
trician, 57,  742,  1906;  J.  RUSSEL,  Proc.  Royal  Soc.,  Edinburgh,  Nov.  20, 
.1905.  E.  WILSON,  Electrician,^  51,  330,  1897,  was  probably  the  first  to 
describe  a  magnetic  detector. 

252  As  the  magnetic  detector  is  most  sensitive  in  a  definite  portion  of  the  magnetiza- 

tion cycle,  the  magnetic  detector  of  the  so-called  BALSILLIE  system  is  comprised 
of  three  detectors,  of  the  type  shown  in  Fig.  317,  each  of  which  is  automatically 
connected  into  circuit  at  the  moment  when  it  is  in  the  most  sensitive  part  of 
the  magnetization  curve  (Jahrb.,  4,  292,  1911;  El.,  64,  512  et  seq.,  1910). 

253  G.  MARCONI,  Electrician,  54,  825,  1905. 

254  R.  ARNO,  Electrician,  55,  469,  1905;  ETZ,  1904,  480.     J.  A.  EWING  and  L.   H. 

WALTER,  Proc.  Roy.  Soc.,  73,  120,  1904.  L.  H.  WALTER,  Proc.  Roy.  Soc.,  77, 
538  et  seq.,  1906.  W.  PEUCKERT,  ETZ,  1904,  992.  A.  G.  Rossi,  Phys. 
Zeitschr.,  10,  549,  1909.  R.  A.  FESSENDEN,  D.R.P.,  227102  (1909). 

255  Review  of  a  large  number  of  articles  dealing  with  the  action  of  the  coherer  in 

note247  and  also  by  P.  WEISS,  Journal  de  Phys.  (4),  5,  462,  1906.  A.  BLANC, 
Journal  de  Phys.  (4),  4,  743,  1905. 

256  German  patent  application  by  A.  KOEPSEL  in  1902.     O.  LODGE  and  A.  MUIRHEAD, 

Electrician,  50,  930,  1903. 
267  L.  H.  WALTER,  Jahrb.,  2,  120,  1908;  Electrician,  61,  683,  1908. 

258  J.  E.  IVES,  Jahrb.,  4,  112,  1910. 

259  Regarding  the  liquid  barretter  see  S.  M.  KINTNER,  Proc.  Amer.  Inst.  El.  Engrs., 

26,  65  et  seq.,  1907.     J.  E.  IVES,  Phys.  Zeitschr.,  11,  1181,  1910. 
26°  Jahrb.,  5,  432,  1912. 

261  Also  see  C.  TISSOT,  Electrician,  60,  25,  1907;  C.  R.,  145,  226,  1907.     J.  S.  SACHS, 

in  Jahrb.,  1,  584  et  seq.,  1908,  quotes  additional  articles  on  the  action  of  the 
electrolytic  detector. 

262  R.  FESSENDEN,  ETZ,  1905,  950. 

263  F.  BRAUN,  ETZ,  1906,   1199;  Electrician,  58,  569,  1907.     PSILOMELAN  detector, 

Jahrb.,  4,  432,  1911.  DUNWOODY  detector,  El.  World,  48,  370,  1906.  G.  W. 
PIERCE  detector,  Lum.  el.,  1,  92,  1908;  Jahrb.,  3,  370,  1910.  G.  J.  PICKARD 
detectors,  Jahrb.,  3,  430,  1910;  Lum.  el.,  11,  172,  1910  (article  by  P.  BRENOT). 
W.  H.  ECCLES,  EL,  60,  588,  1908. 

264  Regarding  the  action  of  crystal  detectors  see  G.  W.  PIERCE, l  H.  SUTTON,  EL,  69, 

66,  1912.  C.  TISSOT,  1'Electricien,  39,  331,  1910.  R.  H.  GODDARD,  Phys. 
Rev.,  34,  423,  1912. 

265  J.  A.  FLEMING,  Proc.  Roy.  Soc.,  74,  476,  1905;  El.  55,  303,  1905.     Data  relative  to 

incandescent  lamp  type  of  detectors  and  their  connections  in  Electrician,  61, 
804,  843,  1006,  1908;  62,  211,  1908;  63,  504,  1909;  64,  68,  1909.  Review  of 


424  WIRELESS  TELEGRAPHY 

various  detectors  with  rarified  gases:  C.  TISSOT,  EL,  58,  729,   1907;  ETZ, 
1908,  172. 

266  A.  WEHNELT,  Ann.  Phys.,  19,  153,  1906. 

267  H.  BRANDES,  ETZ,  1906,  p.  1015. 

268  Jahrb.,  3,  429,  1910  and  Q.  MAJORANA,  Jahrb.,  2,  347  et  seq.,  1909. 

269  P.  LUDEWIG,  Jahrb.,  3,  411,  1911  (electrolytic  cell);  G.  W.  PIERCE,  Jahrb.,  3,  498, 

1910;  El.  Review,  28,  56  et  seq.,  1909;  El.,  64,  183  et  seq.,  1909  (electrolytic 
cell);  El.,  64,  425,  1909  (crystal  detectors).  K.  BANGERT,  Phys.  Zeitschr., 
11,  123  et  seq.,  1910  (galena  detector).  L.  W.  AUSTIN,  Bull.  Bur.  Stands., 
6,  No.  1,  1908.  W.  H.  ECCLES,  El.,  65,  735,  1910;  EL,  66,  166  et  seq.,  1910. 

270  Compare  C.  TISSOT,  Electrician,  58,  730,  1907;  60,  25,  1907.     J.  A.  FLEMING.! 

271  Apparatus  or  methods  for  testing  detectors  described  in  the  following:  J.   A. 

FLEMING  and  G.  B.  DYKE,  EL,  63,  216,  1909.  P.  JEGOU,  ETZ,  720,  1908. 
The  commercial  form  of  detector  testing  apparatus  of  the  TELEFUNKEN  Co. 
is  described  in  Jahrb.,  6,  391,  1913. 

272  Jahrb.,  4,212  et  seq.,  1910. 

273  COUNT  ARCO.160     G.  EICHHORN,  Jahrb.,  6,  301  et  seq.,  1911.     For  other  proposed 

method  for  sound  intensification,  see  P.  JEGOU,  1'Electricien,  37,  129,  1910. 
HENRY,  1'Electricien,  38,  11,  1910. 

274  Phys.  Zeitschr.,  13,  38,  1912. 

275  For  further  details  see  H.  SIMON,  Jahrb.,  2,  409  et  seq.,  1909. 

276  Bulletin  No.  12  of  the  TELEFUNKEN  Co.     Capillary  relay  of  ARMSTRONG-ORLING, 

ETZ,  1906,  p.  385.  M.  CANTOR  had  already  constructed  a  similar  relay  as 
early  as  1900. 

277  COUNT  ARCO.160     G.  EICHHORN,  Jahrb.,  4,  405  et  seq.,  1911.     Also  see  ETZ,  32, 

776,  1911.  Regarding  proposal  of  C.  LORENZ  to  use  a  selenium  cell  see 
Jahrb.,  3,  622,  1910. 

278  J.  TAYLOR,  EL,  41,  278  et  seq.,  1911.     GRUNICKE,  ETZ,  32,  64,  1911.     TH.^BAKER, 

ETZ,  32,  696,  1911  and  EL,  67,  363,  1911. 

279  See  EL,  54,  825,  1905;  63,  908,  1909;  1'Electricien,  39,  93,  1910;  Jahrb.,  4,  524,  1911. 

ETZ,  32,  1164,  1911. 

280  MARCONI,  in  some  of  his  stations,  makes  use  of  the  so-called  "earth  arrester," 

which  consists  in  the  main  of  two  metal  plates  close  together,  inserted  in 
the  ground  connection  of  the  antenna  and  having  the  receiving  circuit  in 
parallel  thereto.  When  transmitting  the  spark  resulting  between  these 
plates  short-circuits  the  receiving  circuit.  As  soon  as  transmission  is  over 
the  receiving  system  is  back  in  circuit.  See  E.  NESPER.ISI 

281  G.  O.  SQUIER,  Electrician,  54,  SZQetseq.,  1905;  56,  453,  1905. 

282  See  R.  RiiDENBERG,  Ann.  Phys.,  25,  446,  1908.     Also  see  H.  BARKHAUSEN,  Jahrb., 

2,  40,  1908;  5,  261,  1912. 

283  J.     ERSKiNE-MuRRAY.1     This    also    shows    illustrations    of    LODGE-MUIRHEAD 

apparatus. 

284  F.  BRAUN,  D.R.P.  136641  (1901). 

285  F.  KIEBITZ,  ETZ,  33,  132,  1912.     K.  BANGERT,  Phys.  Zeitschr.,  11, 123  et  seq.,  1909. 
2850  A  great  number  of  methods  for  making  use  of  the  two  coupling  waves  have  been 

proposed.  J.  A.  FLEMING  (EL,  63,  333,  1909)  e.g.,  proposes  to  use  an  ar- 
rangement like  Fig.  391;  but  one  portion  shall  be  tuned  to  one  wave,  the 
other  portion  to  the  other  wave.  The  currents  of  the  two  detectors  act 
upon  the  same  telephone,  which  has  two  windings  for  this  purpose.  Probably 
no  such  arrangement  has  ever  been  used  in  practice. 

^H.  RIEGGER,  Jahrb.,  5,  35,  1911.  For  the  theory  of  three  very  loosely  coupled 
circuits  see  B.  MACKU,  Jahrb.,  4,  188,  1911.  P.  O.  PEDERSEN,  Jahrb.,  3, 
283,  1910;  4,  449,  1911.  F.  MULLER,  Jahrb.,  6,  13,  1912. 


BIBLIOGRAPHY  AND  NOTES  ON  THEORY  425 

™  ETZ,  33,  376,  1912. 

288  L.  W.  AUSTIN,  Bull.  Bur.  Stands.,  7,  301,  1911. 

289  M.  WIEN,  Ann.  Phys.,  8,  696,  1902.     Experiments  of  L.  MANDELSTAM  and  H. 

BR ANDES  at  the  Strassburg  Forts  in  the  summer  of  1902. 

290  R.  FESSENDEN,  El.  Rev.,  59,  77  et  seq.,  1906;  Electrician,  62,  172,  1908;  65,  314  et 

seq.,  1910.  The  use  of  a  number  of  condenser  circuits  in  the  receiver  for  the 
purpose  of  increasing  the  sharpness  of  resonance  has  been  proposed  by  both 
J.  S.  STONE  and  the  MARCONI  Co.  (Electrician,  62,  171,  1908). 

291  F.  BRAUN,  address  at  Strassburg,  1905. 

292  COUNT  VON  ARCO,  ETZ,  31,  506  et  seq.,  1910;  Jahrb.,  4,  79  et  seq.,  1910. 

293  Regarding  atmospheric  disturbances  see  J.  ERSKINE- MURRAY,  Jahrb.,  5,  108,  1911. 

P.  SCHWARZHAUPT,  EL,  65,  820,  1910.  J.  E.  TAYLOR,  EL,  66,  1022,  1911. 
W.  H.  ECCLES  and  H.  M.  AIREY,  Proc.  Roy.  Soc.,  85,  145,  1911.  A.  ESAU, 
Phys.  Zeitschr.,  12,  798,  1912.  F.  G.  LORING,  EL,  67,  27,  1911.  M. 

DlECKMANN.151 

294  See  J.  ERSKiNE-MuRRAY,1  EL,  68,  465,  1911. 

295  See  Jahrb.,  4,  404,  1911. 

2950  In  the  "reducteur  d'interference"  of  the  BALSILLIE  System  (Lum.  el,  9, 404,  1910) 
a  highly  damped  condenser  circuit  is  coupled  with  the  antenna.  It  is  tuned 
to  the  frequency  of  the  interfering  station  and  is  intended  to  absorb  the 
oscillations  caused  by  it  in  the  receiver. 

™  L'Electricien,  41,  278,  1911. 

2960  R.  FESSENDEN,  El.  Rev.,  59,  38,  1906. 

297  A.  BLONDEL,  Compt.  rend.,  130,  1383,  1900. 
2970  M.  WIEN,  Phys.  Zeitschr.,  13,  1034,  1912. 

298  ANDERS  BULL,  Electrician,  54,  142,  1904.     Regarding  the  HOVLAND  apparatus  see 

Jahrb.,  5,  394,  1912. 

299  E.  NESPER,  Jahrb.,  4,  534  et  seq.,  1911. 

300  Jahrb.,  1,  430,  1908;  2,  419,  1909. 

301  Regarding  "ticker"  and  ticker  connections  see  Jahrb.,  1,  144,  1907.     E.  NESPER, 

Jahrb.,  4,  317,  547,  1911.  H.  MOSLER,  ETZ,  32,  1027,  1911.  F.  KIEBITZ, 
ETZ,  33,  132,  1912. 

302  Jahrb.,  5,  113,  1911. 

303  L.  W.  AUSTIN,  Phys.  Zeitschr.,  12,  867,  1912. 

304  Electrician,  59,  985,  1907;  El.  Rev.,  60,  251  et  seq.,  329,  368  et  seq.,  1907.     Report 

of  DE  FOREST  on  tests  with  this  detector  in  Electrician,  60,  135,  1907. 

305  R.  GOLDSCHMIDT,  EL,  68,  464,  1911;  Jahrb.,  5,  341,  1911. 

306  See  E.  BELLINI,  Jahrb.,  2,  381  et  seq.,  1909  and  L.  H.  WALTER,  EL,  64,  790  et  seq., 

1910.     In  these  articles  a  large  number  of  distance  effect  characteristics  are 
calculated  and  plotted. 

307  If  r  represents  the  distance  between  the  points  P  and  0  (Fig.  405),  then,  under  the 

assumptions  of  Fig.  406,  the  field  of  antenna  B  at  the  point  P  is  of  the  form 

v     •    f          27rr 
Eo  sin 


that  of  antenna  A  is  of  the  form 


whence  the  resultant  field  is  of  the  form 


426  WIRELESS    TELEGRAPHY 

It  follows  from  this  that  the  amplitude  of  the  resultant  field  is 
<p  -\-  \!/  Vird  \l/~\ 

Er0  =  2E0  cos  — jp-  =  2E0  cos  h^-  cos  #  +  | 

This  expression  determines  the  distance  effect  characteristic. 

308  See  J.  A.  FLEMING.1     S.  G.  BROWN,  English  patent  14449  (1899).     A.  BLONDEL41 

and  Lum.  el.,  16,  7,  131,  1911. 

309  Regarding  the  BELLINI  and  Tosi  methods  see  Jahrb.,  2,  239  et  seq.,  381  et  seq.,  511 

et  seq.,  609  et  seq.,  1909;  3,  571  et  seq.,  595  et  seq.,  1910.  Societe  Internationale 
des  electriciens.  Extrait  du  Bulletin  (2)  8,  No.  80,  El.  65,  861,  1910;  67,  66, 
1911. 

310  Jahrb.,  2,  190  et  seq.,  1909. 

311  F.  BRAUN,  Jahrb.,  1, 1,  1907;  Electrician,  67,  222  et  seq.,  244  et  seq.,  1906. 

312  Lum.  el.  (2),  13,  227  et  seq.,  1911. 

313  L.  MANDELSTAM  and  N.  PAPALEXI,  Phys.  Zeitschr.,  7,  303,  1906.     Also  see  A. 

JOLLOS,  Diss.  Strassburg,  1907  and  M.  DIECKMANN,  Diss.  Strassburg,  1907. 

314  Proc.  Roy.  Soc.,  77,  413,  1906;  Electrician,  57,  100,  1906.     Data  on  transatlantic 

stations  at  CLIFDEN  and  GLACE  BAY  in:  Electrician,  60,  883,  1908.  According 
to  F.  GALLIOT  (Electrician,  57,  183,  1906)  similar  experiments  were  made  by 
GARCIA  as  early  as  1900.  K.  E.  F.  SCHMIDT  in  Phys.  Zeitschr.,  8,  5,  1908  pro- 
posed the  use  of  a  directive  transmitter  having  a  vertical  portion  and  a  ground 
network  extending  only  in  one  direction.  Experiments  with  various  antennae 
with  horizontal  parts  described  by  F.  KIEBITZ,  Ann.  Phys.,  32,  941,  1910. 

315  MONCKTON,  Radiotelegraphy,  p.  144. 

316  Diss.  Munchen,  1911;  Jahrb.,  5,  14  et  seq.,  188  et  seq.,  1911. 

317  As  early  as  1901  DE  FOREST  had  already  called  attention  to  the  fact  that  horizontal 

antennae  can  be  used  with  directive  receivers.  See  J.  A.  FLEMING,1  G.  W. 
PICKARD,  Electrician,  59,  564,  1907.  Regarding  the  action  of  the  bent  MAR- 
CONI antenna  as  a  receiver,  see  J.  ZENNECK,  Phys.  Zeitschr.,  9,  50  et  seq.,  1908. 

318  Regarding  earth  antennae  and  their  history,  see  L.  ZEHNDER,  Jahrb.,  5,  594,  1912. 

F.  KIEBITZ,  Verhandl.,  Jahrb.,  5,  360,  1912;  6,  1,  1912.  Also  seeETZ,  33, 
139,  1912;  El.,  68,  936,  978,  1020,  1912.  F.  BRAUN,  Jahrb.,  5,  586,  1912. 

319  L.  W.  AUSTIN,  Jahrb.,  5,  419,  1912.     Austin  states  that  the  energy  of  waves  from 

CLIFDEN  measured  at  Brant  Rock  is  greater  than  would  correspond  to  the 
height  of  the  Clifden  antenna  and  the  energy  used  at  Clifden.  However,  the 
assumptions  on  which  his  calculations  are  based  are  rather  doubtful. 

320  J.  E.  TAYLOR293  points  out  the  particular  freedom  from  interference  of  certain 

arrangements  similar  to  those  of  BELLINI  and  Tosi. 

321  Instead  of  adjusting  the  receiver  for  minimum  or  maximum  sound  intensity,  the 

direction  of  the  transmitter  can  be  determined  by  measuring  the  current  effects 
produced  in  the  detector  circuits  of  two  receivers  and  finding  their  ratio.     See 
El.,  65,  898,  1910  and  A.  BLONDEL308  and  Jahrb.,  2,  190  et  seq.,  1909. 
322 1'Electricien,  39,  177,  1910.     P.  BRENOT,  Lum.  el.  (2),  11,  174,  1910. 

323  EL,  64,  833,  1910. 

324  See  TELEFUNKEN  pamphlet  entitled  "TELEFUNKEN  Kompass." 
3240  A.  ARTOM,  EL,  69,  370,  1912. 

325  General  treatment:  E.  RUHMER,  "Drahtl.  Tel."  (Berlin,  1907).     W.  E.  ECCLES, 

EL,  62, 212  et  seq.,  1908.  G.  EICHHORN,  "  Technische  Mitteilungen,"  Vol.  XXV 
Zurich,  1908.  R.  A.  FESSENDEN,  EL,  59,  985  et  seq.,  1907;  El.  Rev.,  60,  251 
et  seq.,  329  et  seq.,  368  et  seq.,  1907;  EL,  61,  441, 787, 828, 867, 1908.  E.  NESPER, 
Jahrb.,  3,  83  et  seq.,  1909.  Demonstration  apparatus  of  E.  HUTH,  Jahrb.,  3, 
511,  1910.  On  the  theory  of  radio-telephony  see  P.  O.  PEDERSEN,  Jahrb.,  5, 
449,  1912. 


BIBLIOGRAPHY  AND  NOTES  ON  THEORY  427 

326  A.  F.  COLLINS,  Jahrb.,  4,  211,  1911;  EL,  64,  850,  1910;  ETZ,  32,  835,   1911.     M. 

COLIN  and  R.  JEANCE,  EL,  63,  511,  1909.  W.  DUBILIER,  EL,  67,  739,  931,  1911, 
1'Electricien,  41,  231,  1911. 

327  Jahrb.,  5,  237,  1912.     Also  see  DE  FOREST,  Jahrb.,  3,  404,  1910. 

328  E.   NESPER.325 

329  See  G.  SEIBT,  Jahrb.,  3,  202,  1909.     C.  TISSOT,  C.  R.,  149,  281,   1909;  Jahrb.,  3 

189,  1909. 

If  /  is  the  antenna  current,  8,  the  e.m.f.  acting  upon  it,  R  the  resistance  of 
the  microphone  or  the  equivalent  resistance  of  the  microphone  circuit  and 
Ra  the  effective  resistance  of  the  antenna,  then  (assuming  extremely  loose 
coupling  and  primary  circuit  in  tune  with  the  antenna)  we  have 


So      R/Ra         dR 
Ra  L        fl\2     R 


For  a  certain  value  of  ~p,  i.e.,  for  a  certain  relative  change  in  the  microphone 

resistance  this  becomes  a  maximum  for  R  =  Ra. 

330  ETZ,  33,  205,  242,  1912. 

331  J.  MAJORANA,  1'Electricien,  37,  257,  1909;  Lum.  el.  (2),  11,  246  et  seq.,  275  et  seq., 

1910. 

332  EL,  65,  560  et  seq.,  1910. 

333  Jahrb.,  1,  420  et  seq.,  1908. 

334  Jahrb.,  2,  243,  1909  (Amalgamated  Radiotel.  Co.). 

335  O.  SCHELLER,  Jahrb.,  3,  533,  1910. 

336  COUNT  ARCO,  Jahrb.,  4,  79  et  seq.,  1910. 

337  A.  MEISSNER'S  method  consists  in  the  main  of  the  following:  A  number  of  spark 

gaps  in  series,  whose  number  and  gap  length  are  so  chosen  that  the  voltage  of 
the  generator  or  transformer  is  not  able  to  jump  across  them  is  employed. 
If,  however,  one  or  more  of  these  gaps  is  bridged  by  means  of  an  auxiliary  exci- 
tation, a  discharge  takes  place  across  the  entire  series. 

With  direct-current  operation,  this  method  makes  it  possible  to  obtain  an  ab- 
solutely regular  discharge  rate.  For  this  purpose  it  offers  a  more  simple  means 
than  a  rotating  gap  and  moreover  is  adaptable  to  very  low  voltages.  See.344 

338  V.  POULSEN,  Jahrb.,  2,  419,  1909. 

339  S.  EISENSTEIN,  Jahrb.,  2,  417,  1909.     H.  REIN,  Jahrb.,  4,  196,  1911. 

340  Jahrb.,  5,  118,  1911;  D.R.P.,  227989  (1910). 

341  D.R.P.,  245445  (1912). 

342  J.  ZENNECK,  Wied.  Ann.,  69,  858,  1899.     This  same  method  later  became  the  basis 

of  U.  S.  Patent  of  H.  SHOEMAKER  and  H.  CLYDE  SNOOK  (No.  736884,  1903). 

343  D.R.P.,  149761  (1902). 

344  COUNT  ARCO,  Address  before  convention  of  "Naturforscher,"  Minister,  1912. 

345  J.  ZENNECK,  Phys.  Zeitschr.,  13,  953,  1912. 

346  Regarding  the  efficiency  of  radio-telegraph  stations  from  various  scientific  and 

commercial  points  of  view,  see:  J.  ERSKINE-MURRAY,  Lum.  el.,  16,  331,  1911. 

347  C.  TISSOT  and  F.  PELLIN,  Jahrb.,  2,  525,  1909.     C.  TISSOT,  EL,  67,  333,  1911. 

P.  BRENOT,  Lum.  el.  (2),  12,  368,  1910.  G.  EICHHORN,  Jahrb.,  4,  642  et  seq., 
1911. 

348  Jahrb.,  4,216,  417,  1911. 

349  P.  BRENOT,  Lum.  el.  (2),  12,  387  et  seq.,  1910.     C.  TISSOT,  Jahrb.,  4,  618  et  seq.,  1911. 

350  G.  REMPP,  Experiments  in  Strassburg,  Elsace.     Also  see  EL,  66,  131,  1910.     Re- 


428  WIRELESS  TELEGRAPHY 

garding  other  applications  in  meteorology  also  see  Jahrb.,  2,  529,  1909;  3,  581, 
1910. 

351  Curves  for  determination  of  wave-length  from  capacity  and  self-induction  by  W.  W. 
MASSIE,  EL,  57,  826,  1906. 

362  Recent  articles  on  the  static  characteristic  of  arcs  with  different  electrodes  and 

gases:  W.  L.  UPSON,  EL,  69,  60  et  seq.,  90  et  seq.,  1907.  H.  TH.  SIMON,  Phys. 
Zeitschr.,  8,  471  et  seq.,  1907.  C.  E.  GUYE  and  L.  ZEBRIKOFF,  Phys.  Zeitschr., 
8,  703,  1907.  HEUBACH,  ETZ,  13,  460,  1892.  General:  "Das  elektrische 
Bogenlicht"  by  E.  RASCH  (in  "Die  Elektrotechnik  in  Einzeldarstellungen"). 
Braunschweig,  1910. 

363  See  Notes  44  and  45.     A.  ESAU,  Jahrb.,  6,  212,  378,  1912.     Esau  simplifies  STRAS- 

SER'S  equation  to  the  form: 

L  =  47rrn  jloge  -  +  0.333  +  S 

and  gives  tables  for  the  values  of  S,  which  depends  only  on  jr-  and  n. 

354  EMS,  409  et  seq. 

365  Also  see  L.  W.  AUSTIN  in  Jahrb.,  6,  588,  1913,  which  also  gives  the  maximum  loads 
for  constantan,  manganin,  platinum  and  copper  wires. 


INDEX 


ABHAHAM,  M.,  Field  of  the  lineal  oscil- 
lator, 27,  31,  409 
On  the  general  theory  of  electricity, 

410 
Absorption  of  ions,  97 

of  waves  by  the  earth's  surface,  249 

et  seq. 

Acoustic  resonance,  291  et  seq.,  297,  330 
ADELMANN,    L.,    and   W.   HAHNBMANN, 

409 

Advancing  waves,  26,  29 
Aerials,  various  forms  of,  150 

Air  blowers blasts,  187,  240 

AIREY,  H.  M.,  and  W.  H.  ECCLES,  425 
Airship  antennae,  163,  169 
Airships,  reception  of  messages  in,  302 
ALEXANDERSON,  E.  F.  W.,  213 
ALGERMISSEN,  J.,  412 
Alternating  current  operation,  195 
resistance,  48 
magnetic  field,  2 
Alternators,  High  frequency,  213  et  seq., 

371 

Amplitude,  11,  12 
curve,  12 

of  condenser  circuits  with  spark 

gap,  13 

without  spark  gap,  11 
ANDERLE,  A,  408 
ANDERSON,  H.,  408 
Antenna?,  150  et  seq.,  382 
artificial,  169 
bent  Marconi,  356  et  seq. 
damping  of,  167 
directive,  341  et  seq.,  356  et  seq. 
effective  capacity  of,  165 

self-induction  of,  164 
horizontal,  364 

with  increased  end  capacity,  152 
with  reduced  radiation  damping,  166 
Anti-coherers,  279 
Anti-node  of  current,  25 

of  potential,  25 
Arc,  constants  of  the,  392 


Arc,  generation  of  undamped  oscillations 

by  the  Poulsen,  220  et  seq. 
hysteresis,  232 
oscillations,   use  of,   for  measuring 

purposes,  116,  119,  121,  225 
the  term,  defined,  245 
ARCO,  COUNT  G.  VON,  Call  signal,  Sound 

intensifier,  424 

Connections  for  receiving,  313 
Data  regarding  Telefunken  stations, 

167,  417 
Duplex    reception    with    one    wave 

length,  425 

Frequency  transformation,  380  et  seq. 
High  frequency  alternator,  219,  380, 

419 

Sensitiveness  of  detectors,  289 
ARMSTRONG-ORLING,  424 
ARNO,  R.,  275,  413 
ARTOM,  A.,  Determination  of  location  by 

radio-telegraphy,  368,  426 
Atmosphere,  effect  of,  upon  wave  propa- 
gation, 263 

Atmospheric   disturbances  and  methods 
for  counteracting,  324,  326,  332 
Audion,  285,  377 
AUSTIN,  L.  W.,  Antennae  measurements, 

418 

Brant  Rock  station,  417 
Brush  discharge  in  condensers,  141 
Condensers  in  high  frequency  cir- 
cuits, 409 

Coupled  receivers,  425 
Detectors  and  measurements  there- 
with, 273  et  seq.,  413,  423 
Resistance  wires,  428 
Rotating  ticker,  335 
Thermocouple,  75 
Wave    propagation    measurements, 

258,  265,  269,  421,  426 
Wireless  telephony,  371 
Automatic  key,  203 
Auxiliary  cell  or  element,  284,  290 

excitation  for  quenched  gap  trans- 
mitter, 378 
AYRTON,  H.,  392 
429 


430 


INDEX 


BADISCHB    ANILIN-     UND     SODAPABRIK, 

Quenched  spark  gap,  187 
BAKER,  TH.,  424 
BALSILLIE  system,  207,  425 
BANGERT,  K.,  Detectors,  424 

Receiver  connections,  424 
BARKHAUSEN,  H.,  Action  of  receivers,  424 
Arc     method     for    generating     un- 
damped  oscillations,   231,    234, 
420,  421 

Radiation  resistance  of  antennae,  410 
Spark  gap  resistance,  15 
BARRECA,  P.,  Ground  resistance,  417 

Radiation    of    open    oscillators    and 

antennae,  410 
Barretter,  72,  77,  272 
BEGGEROW,  H.,  Airship  antenna,  163 
BELLINI,  E.,  Distance  effect  characteris- 
tics, 425 

and  A.  Tosi,  Arrangements  for 
directive  telegraphy,  347  et  seq., 
367  et  seq. 

BENISCHKE,  G.,  415 
Bent  Marconi  antenna,  356  et  seq. 
BETHENOD,    J.,    Effective    resistance    of 
rectangular  wires  and  strips,  412 
Resonance  inductor,  415 
BIERLEIN,  W.,  415 

Bilateral  transmitter  for  directive  teleg- 
raphy, 345 

BlRKELAND,   K.,  421 

BJERKNES,  V.,  Loose  coupling  of  oscil- 
lators, 85 

Resonance  method,  113,  114,  118 
BLACK,  TH.  P.,  411 
BLANC,  A.,  423 
Block  condenser,  64,  290 
BLONDEL,    A.,    Antenna   with   increased 
end  capacity,  411 

Arc  generator,  420 

Directive  transmitter,  345  et  seq.,  426 

Mechanical  tuning,  331 

Part  played  by  upper  layers  of  the 
atmosphere,  422 

Studies  of  the  arc  method,  231,  236 

Tone  transmitter,  377 

Waves  produced  by  grounded  an- 
tenna, 421 

Blowers,  air,  187,  240 
Blow-out,  magnetic,  187,  240,  242  et  seq. 
BOAS,  H.,  Coherer,  278 


BOAS,  H.,  Condensers,  60,  140 

Incandescent  lamp  oscillograph,  4 
Quenched  spark  gap,  95 
Resonance  inductor,  198,  415 
Rotating  mirror  for  high  speeds,  4 
Bolometer,  72,  77,  272 
Boulogne,    station    for    directive    teleg- 
raphy, 351 
Braided  wire,  48,  49 
Braids  of  individually  insulated  wires,  48, 

49 

BRANDES,  H.,  Action  of  detectors,  284 
Determination  of  the  decrement,  116 
Thermocouple,  75,  77,  413 
and  L.  MANDELSTAM,  Coupling  for 

tuned  telegraphy,  322 
BRANLY,  277 

Brant  Rock  station,  152,  165 
BRAUN,  F.,  Braun  transmitter,  175,  184, 

209 

tube,  2,  231 

Directive  telegraphy  employing  sev- 
eral antennae,  352 
inclined  antennas,  363 
Energy  connections,  so-called,  178 
Ground  antenna,  426 
Hot-wire-air  thermometer,  71 
Psilomelan  detector,  282 
Receiver  connections,  311 
Sparkless  key,  203 
Triplex  reception  using  one  antenna, 

425 

Breakdown  voltage,  64,  232,  399 
BREDOW,  H.,  417 
BRENOT,    P.,    Arc  generator  of  Blondel, 

420 

Eiffel  Tower  station,  412 
Experiments  with  Bellini  and  Tosi 

arrangements,  367 
Frequency  meter  of  Ferrie,  412 
Longitude    determination    by    radio 

telegraphy,  427 
Radio  time  signals,  427 
Resonance  inductor,  History  of  the, 

415 

BRION,  B.  G.,  419 
BROWN,  S.  G.,  Detector,  282 
Directive  transmitter,  345 
Telephone  relay,  291 
Brush  discharge  of  antennae,  167,  168 
of  coils,  34 
of  condensers,  21,  86 
insulation  against,  168 


INDEX 


431 


BRYLINSKY,   Resistance  with  oscillating 

currents,  412 
BULL,  A.,  332 
BURSTYN,  W.,  Ground  currents,  ground 

resistance,  417 
Key  arrangement,  419 
Multitone  transmitter,  229 
Rotating  spark  gap,  419 


Call   signal,    apparatus  for  calling,  299, 

300 

CAMPBELL,  A.,  416 
CANTOR,  M.,  424 
Capacity,  determination  of,  112 

Effective,    of    open    oscillators     or 
antennae,  40,  164,  165 

End,  of  open  oscillators  or  antennae, 
41,  42 

in  the  arc  transmitter,  227,  241 

of  coils,  113 

of  condensers  in  oscillation,  8 

resultant,  6 

unit  of,  6 

Carbon  coherer,  279 
Carborundum  detector,  282,  286  et  seq. 
CASTELLI,  Mercury  coherer,  278 
Cathode  ray  tube,  2 
CHAPFEE,  E.  L.,  184,  408 
CHAMBERS,  F.  J.,  374 
Characteristic  of  the  arc,  231  et  seq. 

of  detectors,  285  et  seq. 

of  the  distance  effect,  338,  342  et  seq. 
Charging  stage  in  the  arc  method,  235 
Choke  coils,  64,  199,  291,  323 
Circuit  losses,  ^.38 
Clifden,  station  at,  266  et  seq. 
Close  coupling,  81,  87  et  seq. 
Closed  oscillator,  oscillating  circuit,  24 
CLYDE,  H,  427 

Coastal  contour,  effect  of,  on  wave  propa- 
gation, 263 
COFFIN,  393 
COHEN,  B.  S.,  73,  413 
COHEN,  L.,  Effective  resistance  of  coils, 
412 

Theory  of  coupled  circuits,  415 
Coherers,  276  et  seq. 
COHN,  E,  408 

Coils,  effective  resistance  and  self-induc- 
tion of,  47  et  seq. 

having  adjustable  self-induction,  51 


Coils  in  open  oscillators  and  antennae,  44 

et  seq.,  165 

natural  oscillations  of,  33 
various  forms  of,  50  et  seq. 
COLIN,  M.,  and  R.  JEANCE,  371 
COLLINS,  A.  F.,  371 
Compass,  radio,  368  et  seq. 
Compressed  air  or  gas  condensers,  55,  57, 

179 

spark  gaps,  418 
Condenser  circuits,  natural  frequency  of, 

5,  384 

oscillations  of,  1  et  seq. 
wave  length  of,  5,  386 
Condensers,  adjustable,  59  et  seq. 
brush  discharge  in,  21,  138  etseq. 
in  open  oscillators,  or  antennae,  41, 

165 

losses  in,  20,  138 
various  forms  of,  54  et  seq.,  179 
Conductivity  of  earth  and  water,  248 
Conical  antenna,  151,  169 
Continuous  oscillations.     See  Undamped 

oscillations. 

CORBINO,  O.  M.,  Arc  method,  420 
High  frequency  generator,  420 
Counterposie,  157 
Coupled  circuits,  79  et  seq.,  142  et  seq. 

transmitters,  175  et  seq.,  208 
Coupling,  capacity  or  electric,  81 
close,  81 
coefficient  of,  82 

conductive,  direct  galvanic,  79,  80 
critical  degree  of,  96,  149 
degree    or  percentage   of,    89,    401, 

402 

in  Braun  transmitter,  176  et  seq. 
in  Wien  transmitter,  184,  185 
devices  and  arrangements  for,  82  et 

seq. 

inductive  or  magnetic,  79 
loose,  81 
of  damped  oscillating  circuits,  84  et 

seq. 

of  undamped  oscillating  circuits,  99 
et  seq. 

oscillations waves,  88 

Crystal  detectors,  282  et  seq. 
Cullercoats,  station  at,  225,  302 
Current,  anti-node  of,  25 
curve,  2 

distribution,  curve  of,  24,  25,  155 
effect,  67 


432 


INDEX 


Current,  measurement  of,  67  et  seq. 

node  of,  25 

path,  1,  179 
Curvature  of    earths  surface,  effect  of, 

on  wave  popagation,  255 
Cylindrical  coils,  52,  393 


Damped  oscillations,  2 
Damping,  2,  5,  9  et  seq. 

causes  of,  11,  40,  41,  167  et  seq. 
of  antennae,  167  et  seq. 
of  condenser  circuits,  9  et  seq. 
Daylight,  effect  of,  on  wave  propagation, 

265  et  seq. 

Decrement,  joulean,  12,  167 
lineal,  14 
logarithmic,  12 
measurement  of  the,  113  et  seq.,  118 

et  seq.,  125  et  seq.,  135 
total,  15 

Decrements,  oscillation    curves   for   va- 
rious, 389  et  seq. 
Decremeter,  126 

Deionization  of  a  spark  gap,  97,  98 
Detector  circuit  in  the  receiver,  310,  313, 

375 
Detectors,  272  et  seq. 

action  of,  282,  283,  287  et  seq. 
crystal,  282 
efficiency  of,  287 
electrolytic,  280 
magnetic,  274 
overloading,  301 
sensitiveness  of,  289 
thermal,  272 

used  for  measuring  current,  76,  78 
DIECKMANN,  M.,  Measurements  with  the 
Mandelstam       and       Papalexi 
method,  426 
Wireless    telegraphy    in    connection 

with  airships,  418 
Dielectric  constant,  determination  of,  112 

of  soils,  etc.,  248 
hysteresis,  losses  due  to,  20,  138 
DIESSELHORST,    H.,    Frequency   of   con- 
denser circuits,  408,  416 
Oscillograph  records,  4,  89,  415 
Diffusion  of  ions,  97 
Direct  coupling,  80,  175  et  seq.,  311 

current  operation  of  radio  apparatus, 
194,  198,  199 


Directive  power  of  a  transmitter,  338 

telegraphy,  338  et  seq.,  365  et  seq.,  381 
Discharge  analyzer,  69 

frequency,  68,  69,  211,  378 
potential,  64,  232,  399,  400 
retardation  of  the,  65,  208 
Discharging  stage  in  the  arc  method,  235 
Dissonance,  necessary,  316,  318 
Distance  effect  of  open  oscillators  and 

antennae,  35  et  seq.,  156 
characteristic,  338 

of  bent  Marconi  antenna,  356 

et  seq. 

of  several  antennae,  342  et  seq. 
measurement  of  wave  length  at  a, 

329 

DOENITZ,  129 
DOLEZALEK,  F.,  49 
DORN,  E.,  108 
Double  antennae,  341  et  seq. 
cone  antenna,  151,  169 
DOWSE,  C.  M.,  413 
DRUDE,  P.,  Coupled  circuits,  90  et  seq. 

Oscillations  of  coils,  409 
DUBILIER,  W.,  371 

DUCRETET,  F.,  and  E.  ROGER,  Conden- 
sers, 179 

Experiments    with    coupled    trans- 
mitters, 175 

Rotating  spark  gap,  204  et  seq. 
DUDDELL,  W.,  Arc  method,  221,  231,  420 
Thermal  galvanometer,  75,  272 
Undamped  oscillations,  419 
and  J.  E.  TAYLOR,  Experiments  on 
wave  propagation,  260,  269,  272 
DUNWOODY,  282 
Duplex  reception,  323  et  seq. 

transmission,  325 

DYKE,  G.  B.,  and  J.  A.  FLEMING,  409,  424 
Dynamic  characteristic  of  the  arc,  231 
Dynamometer,  135  et  seq. 
effect,  132  et  seq. 


E 


Earth.     See    Ground,     ground    currents, 

ground  resistance,  etc. 
arrester,  424 

Earth's  surface,  effect  of,  on  wave  propa- 
gation, 246  et  seq. 
EBERT,  H.,  422 

ECCLES,  W.  H.,  Detectors,  279,  287,  423 
Effect  of  solar  eclipse,  422 


INDEX 


433 


ECCLES,  W.  H.,  Wireless  telephony,  426 
and  H.  M.  AIREY,  Atmospheric  dis- 
turbances, 425 
and  A.  J.  MACKOWER,  Quenched  gap 

transmitter,  419 
Eclipse   of   the    sun,    effect   of,    on   the 

range  of  operation,  266 
Eddy  currents,  22,  120 
EDELMANN,  DR.,  &  SON,  295 
EDWARDS,  W.,  412 
Effective  resistance,  48 
Efficiency  of  antennae,  167 
of  detectors,  287 
of  various  transmitters,  174,  211 
EGER,  F.,  416 

EGNER,  C.,  and  J.  G.  HOLMSTROEM,  373 
EICHHORN,  G.,  Impulse  excitation,  182 
Practical  notes,  424 
Wireless  telephony,  426 
EICKHOFP,  W.,  Brush  discharge  in  con- 
densers, 138,  139 
Points  on  electrodes,  use  of,  123 
Spark  gap  damping,  409 
Eiffel  Tower  station,  49,  165 
EINTHOVEN  string  galvanometer,  296 
EISENSTEIN,  S.,  Rotating  spark  gap,  418 
Spark   gap  for    impulse   excitation, 

183 
Tone    transmitter    with   undamped 

oscillations,  427 

Electric  or  capacity  coupling,  81 
Emergency  or  auxiliary  transmitter,  209 
Energy,  measurement  of,  200  et  seq. 

transfer  of,  between  coupled  oscillat- 
ing circuits,  9,  39 
used  in  radio-telegraphy,  quantities 

of,  381 
EPSTEIN,  J.,  Frequency  transformation, 

379 
EPSTEIN,    P.,    Waves  along  the  earth's 

surface,  250 
Equivalent  resistance  of  a  closed  circuit, 

85,  120 
ERB,  F.,  422 

ERSKINE-MURRAY,  J.,  Cause  of  atmos- 
pheric disturbances,  425 
Efficiency  of  a  radio  station,  427 
"  Handbook  of  Wireless  Telegraphy," 

408 

Radiation  resistance,  169 
ESAU,    A.,    Effective   capacity,    etc.,    of 

antennae,  418 
resistance,  etc.,  of  coils.  411 

28 


ESAU,  A.,  Node  of  potential  in  open  os- 
cillators (antennae),  410 
Self-induction  of  coils,  393,  428 

ESPINOZA  DE  LOS  MONTERAS,  A.,  Instru- 
ments for  measuring  high  fre- 
quency currents,  413 
Quenched  spark  gaps,  95,  98,  415 

Excitation  circuit  of  Braun  transmitter, 
175 

Exponential  curve,  12 

Extremely  loose  coupling,  81 


FEDDERSEN,  W.,  3,  4 
FERRIE,  Electrolytic  detector,  280,  286 
Frequency  meter,  63 
Rotating  spark  gap,  419 
FESSENDEN,  R.  A.,  Barretter,  72,  272 
Compressed  air  condenser,  55,  179, 

412 

Electrolytic  detector,  280  et  seq. 
Heterodyne  receiver,  335 
High  frequency  generator,  213 
Magnetic  detector,  275 
Method  for  securing  secrecy  of  mes- 
sages, 323 

Rotating  spark  gap,  204 
Telephone  relay,  374 
Water  stream  used  as  antenna,  150 
Wireless  telephony,  371 
Field  of  an  open  oscillator,  27,  35 
FISCHER,  C.,  Determination  of  effective 

capacity,  etc.,  of  antennae,  165 
Experiments  with  coupled  circuits, 

91  et  seq.,  142  et  seq.,  415 
Measurements  with  undamped  oscil- 
lations, 416 
FISCHER,  K.,  422 
FITZGERALD,  F.,  420 
Flat  coils,  50,  393 

top  antennae,  152 
FLEMING,  J.   A.,  Air  blowers  for  spark 

gaps,  416 
Condensers    in    oscillating    circuits, 

408 

Degree  of  coupling  in  coupled  trans- 
mitters, 177 
Discharge  analyzer,  69 
Effect  of   ionization  of  the  atmos- 
phere, 265 
of  solar  eclipse,  422 
Gas  detector,  283  et  seq. 


434 


INDEX 


FLEMING,    J.  A.,  Incandescent  filament 

detector,  283  et  seq. 
Oil  condenser,  55 
Oscillations  of  inductive  coils,  409 
Receiver  connections,  424 
"The  Principles  of    Electric    Wave 

Telegraphy,"  408 
Wave  meter,  125 

and  G.  B.  DYKE,  Investigation  of 
insulators  for  oscillating  poten- 
tials, 409 

Testing  detectors,  424 
Flint  glass,  jars  and  condensers  of,  20 
Fluctuation   of  frequency  due  to  brush 
discharge  from  condensers,  138 
et  seq. 

with  the  arc  method,  241 
Fly-wheel  connection,  the  so-called,  166, 

228 
FOREST,   DE,   Detectors,   280,    (audion), 

285 

Interference  of  waves,  422 
Wavemeter,  125 
Form    factor    of    an    open    oscillator    or 

antenna,  37 

FRANKS,  Wavemeter,  129 
Frequency,  determination  of  the,  3  et  seq., 

63,  106  et  seq.,  123  et  seq.,  134 
factor,  8,  137 

of  arc  oscillations,  238  et  seq. 
of  coils,  natural,  33 
of  condenser  circuits,  natural,   5  et 

seq.,  384 

of  open  oscillators  or  antennae,  natu- 
ral, 26,  155,  164 
transformation,  379 

Fundamental    oscillation   of   open   oscil- 
lators, 24,  25 


G 


GALLETTI,  R.  C.,  184 
GALLIOT,  F.,  426 
Galvanic  coupling,  79  et  seq. 
Gap.     See  Spark  gap. 

length,  maximum,  64  et  seq.,  399,  400 
GARCIA,  426 

G!TI,  BELA,  Barretter,  73,  77,  272 
GEISSLER  tube  as  indicator  of  electric 

oscillations,  69 
GEHRKE  incandescent  lamp  oscillograph, 

4,  408 
GEITLER,  J.  VON,  414 


Generators,  high  frequency,  213  et  seq.t 

371 

GERLACH,  W.,  76 
Gesellschaft    fiir   drahtlose   Telegraphic, 

arc  generator,  222 
call  signal  device,  299  et  seq. 
commercial  radio  station  apparatus, 

167,  192  et  seq. 

compass,  Telefunken,  368  et  seq. 
condensers,  56  et  seq.,  60 
detectors,    273,   277,   280,   281,  282 

apparatus  for  testing,  424 
duplex  reception,  324  et  seq. 
interrupter,  183 
multiplex    radio-telegraphy,   324    et 

seq. 
Nauen,  station  at,  64,  152,  165,  168, 

179,  193,  198 
quenched  gap  transmitter,  192 

spark-gap,  122,  189 
receiver  connections,  311  et  seq. 

for  undamped  oscillations,  334 
recording  reception,  297,  298 
relay,  297 

resonance  inductor,  196 
sound  intensifier,  291  et  seq. 
spark-gap  construction,  180,  182 
umbrella  antenna,  152 
variometer,  54 
wavemeter,  125,  129,  183 
GIEBE  standard  condenser,  55 
Glace  Bay,  station  at.     See  Clifden. 
GLAGB,  G.,  Coupling  of  undamped  oscil- 
lations, resonance  inductor,  103 
Equations    for    coefficient    of    self- 
induction   411 
GLATZEL,  B.,  Air  blowers  for  quenched 

spark  gaps,  187 
Hydrogen  spark  gap,  183 
Mercury  arc  lamp  as  quenched  spark 

gap,  415 

GOLDSCHMIDT,  R.,  High  frequency  gen- 
erator, 216  et  seq.,  379 
Receiver  for  undamped  oscillations, 

336 
Tone     transmitter    for    undamped 

oscillations,  378 
GODDARD,  R.  H.,  423 
Goniometer,  radio,  350,  367  et  seq. 
GRANQUIST,  G.,  420 
Graphite  coherer,  279 
GRAY,  A.,  Non-sparking  key,  203 
GROBER,  M.  K.,  416 


INDEX 


435 


Ground  antennae,  364 

currents,  158  et  seq.,  168 

resistance  of  the,  158  et  seq.,  172 

water,  160,  260 

wire  network,  158 
Grounding  of  open  oscillators,  antennae, 

46,  157,  270,  271 

GROVER,  F.  W.,  and  E.  B.  ROSA,  411 
GRUNICKE,  424 

GtJLDENPFENNIG,  O.,   422 

GUYAU,  A.,  411 

GUYE,    C.   E.,   and  L.   ZEBRIKOFF,    Arc 
constants,  392 


II 


HACK,  F.,  Field  of  lineal  oscillator,  27 
Propagation  of  waves  along  earth's 

surface,  260 
HAHNEMANN,  W.,  Fly-wheel  connection, 

420 

Rheostat  for  high  frequencies,  412 
Spark-gap  damping,  409 
and  L.  ADELMANN,  Investigation  of 

condensers,  409 
HARMS,  F.,  409 
Harp-shaped  aerial,  151 
HARTMANN  and  BRAUN  hot-wire  instru- 
ments, 71 

HENRY,  Sound  intensifier,  424 
HERMANN,  K.,  412 

HERTZ,  H.,  Field  of  open  oscillator,  409 
Frequency,   determination   of,  106 
Hertz  oscillator,  41 
Radio  reflector  experiments,  340 
Heterodyne  receiver,  335 
HEUBACH,  Arc  constants,  392 
HEYDWEILLER,  A.,  Dissipation  of  energy 

in  the  spark,  14 

Gap  length   and  breakdown  poten- 
tial, 399,  400,  412 

High  frequency  generators,  213  et  seq. 
speed  telegraph  apparatus,  203,  229, 

302 
Hills,  effect  of,  on  wave  propagation,  258 

et  seq. 

HILLS,  S.  H.,  413 
HIRSCH,  R.,  130 
HOLMSTROM,  J.  G.,  373 
HORSCHELMANN,  H.  VON,  358  et  seq. 
Hot-wire  air  thermometer,  71,  77 

instruments,  71,  77 
HOVLAND,  332 


HUTH,  E.,  Condensers,  55 

Direct  reading  wavemeter,  130 

String  galvanometer,  295 

Wireless  telephony,  426 
Hydraulic  microphone,  373,  374 
Hydrogen  as  used  in  the  arc  transmitter, 
225  et  seq.,  240  et  seq. 

gap,  95,  98,  123 
Hysteresis  decrement,  20 

dielectric,  20,  138 


Ignition  characteristic,  238 

voltage,  64,  232 
Impressed  oscillations,  85 
Impulse  excitation  by  means  of  conden- 
sers, 183 

general  consideration  of,  182 
in  true  sense  of  the  words,  182 
used  for  measuring  purposes,    122, 

182 

Indicating  circuit,  107 
Indicators  of  electromagnetic  waves,  272 

et  seq. 
Induced  currents,  damping  due  to,  23, 

120,  168 
Inductive  coils  for  high  frequencies,  62, 

291,  323 

Initial  amplitude,  13 
Insulation  for  high  frequencies,  66  et  seq. 

of  antennae,  168 
Interference  between  radio  stations,  328, 

336,  366 
preventer,  323 
Intermediate  circuit  in  Wien  transmitter, 

186 

Interrupter  in  the  antenna  for  tone  trans- 
mission, 378 

in  the  supply  circuit,  124,  194 
in  the  receiver,  333 
lonization  of  the  atmosphere,  effect  of, 

on  the  waves,  264  et  seq. 
ISAKOW,  L.,  417 

IVES,  J.  E.,  Detectors,  280  et  seq. 
Wavemeter,  125 


JACKSON,  H.  B.,  259 
JACOVIELLO,  F.,  420 
Jarring,  effect  of,  on  detectors,  301 
JEANCE,  R.,  371 


436 


INDEX 


JEGOU,  P.,  424 

JERVIS-SMITH,  F.,  Compressed    air    con- 
denser, 412 
gap,  418 
Jigger,  308 
JOLLOS,  A.,  417,  426 
JONAS,  G.,  416 

K 

KAISER,  J.,  415 

KALAHNE,  A.,  415 

KANN,  L.,  Dynamometer  effect,  417 

Zero   method   for   determination   of 

decrement,  116 
KEMPE,  W.,  413 
KENNELLY,  A.  E.,  422 
KEY,  2G2 

Relay,  203 
KIEBITZ,  F.,  Arc  generator,  226 

Experiments  on  directive  telegraphy, 
422,  426 

Ground  antennse,  365 
resistance,  417 

Receiver  connections,  424 
KIMURA,  S.,  415 
KINRAIDE,  T.  B.,  418 
KINTNER,  S.  M.,  Bolometer,  423 

Breakdown  potential  and  gap  length, 

412 

KIRCHHOFP'S  "Telegraph  Equation,"  410 
KLEMEN£IC,  Thermocouple,  74 
Knockroe,  station  at,  225,  227 
KOEPSEL,  A.,  Adjustable  condenser,  60 

Coherer,  278,  et  seq. 
KORDA,  412 


LAHMEYER  WORKS,  379 

LANGE,  H.,  418 

Leakage  discharge.     See  Brush  discharge. 

LEBEDEW,  P.,  75 

LECHER,  E.,  Circuit  arrangement,  Le- 
cher's wires,  Lecher's  system, 
110,  163,  249 

Wave    propagation     along     earth's 
surface,  421 

Length  of  gap,  maximum,  64  et  seq.,  399, 
400 

Lengthening  coils,  166 

LENZ,  W.,  411 

LEPEL,  E.  VON,  Quenched  spark  gap  hav- 
ing plate  electrodes,  187 


LEPEL,  E.  VON,  Wireless  telephony,  371 
LINDEMANN,  R.,  Effective  resistance  with 

oscillating  currents,  411  et  seq. 
Measurements  with  undamped  oscil- 
lations, 416 
Lineal  oscillator,  transmitter,  24  et  seq., 

163 

Liquid  barretter,  272 
Load  of  condensers,  so-called  energy  (TFC), 

21 

Location,    determination    of,    by    radio- 
telegraphy,  367  et  seq. 
LODGE,   O.,   Resonance  method   for  fre- 
quency determination,  106 
and    A.    MUIRHEAD,    Counterpoise, 

417 

Mercury  coherer,  278 
Recording      reception,     294     et 

seq. 

Tuned  telegraphy,  310 
Umbrella  antennse,  152 
LOEWE,  S.,  114,  119 
LOEWY,  H.,  421 
Loose  coupling,  81 

of  oscillator  and  closed  circuit,  84 
of  two  oscillators,  85  et  seq. 
with  undamped  oscillations,  100 
LORENZ,  C.,  Adjustable  condenser,  61  et 

seq. 

Call  signal  device,  424 
Coupling  coils,  84 
Discharge  analyzer,  69 
Impulse  spark  gap,  192 
Interrupter,  183 

Multitone  transmitter,  229  et  seq. 
Photographic  recorder,  295 
Poulsen  arc  generator,  222,  229 
Receiver  for  undamped  oscillations, 

333 

Thermal  detector,  273 
Ticker,  334  et  seq. 
Tone     transmitter    for     undamped 

oscillations,  378 
Variometer,  53 
Wavemeter,  125,  183 
LORING,  F.  G.,  419 
LUBOWSKY,  H.,  418 

LUDEWIG,  P.,  Determination  of  decre- 
ment and  degree  of  coupling, 
416 

Experiments  with  detectors,  424 
Radio     communication     with     air- 
ships, 418 


INDEX 


437 


M 


MACDONALD,  H.,  422 
Machines,     high    frequency.     See    Gen- 
erators, alternators. 
MACKOWER,  A.  J.     See  Eccles. 
MACKU,    B.,    Connections  for  quenched 

gap  transmitter,  145 
Coupled  circuits,  145,  415,  417 
Rupture  of  sparks,  117 
Theory  of  the  Goldschmidt  high  fre- 
quency machine,  419 
of  the  resonance  curves,  415 
MADELUNG,  E.,  423 
Magnetic  blow-out,  187,  240,  242  et  seq. 

coupling,  79 
MAJORANA,    Q.,    Hydraulic   microphone, 

373 

Radio-telephony,  371,  373,  377 
MANDELSTAM,  L.,   Plotting  curves  with 

aid  of  Braun  tube,  408 
and  H.  BRANDES,  Loose  coupling  in 

receiver,  322 
and    N.    PAPALEXI,    Dynamometer 

effect  and  its  application,  132 
Production    of    a    desired    phase 

difference,  353 
MARCH,  H.  W.,  256 
MARCONI,  G.    and    MARCONI    WIRELESS 

TEL.  Co.: 

Adjustable  condenser,  61 
Antennae,  151 
Bent  antenna,  356  et  seq. 
Coherers,  277 

Condensers  as  used  in  stations,  179 
Day   and   night   transmission   com- 
pared, 265  et  seq. 
Duplex  and  multiplex  operation,  324 

et  seq. 

Earth  arrester,  424 
Jigger,  transformer  in  the  receiver, 

308 

Magnetic  detector,  274  et  seq. 
Protection  against  atmospheric  dis- 
turbances, 326  et  seq. 
Rapidity  of  telegraphing,  301 
Receivers,  307  et  seq.,  310  et  seq. 
Rotating  spark  gap,  203  et  seq.,  211 
Separated  transmitting  and  receiv- 
ing antennae,  356,  357,  382 
Transatlantic  stations,  199,  208,  227, 

266,  356 
Transmitter,  173,  208  et  seq. 


MARCONI,   G.  and   MARCONI  WIRELESS 

TEL.  Co.: 
Use  of  incandescent  filament  type 

of  detectors,  284 
Wavemeter  (and  decremeter),  125  et 

seq. 

MARESCA,  409 
MASSIE,  W.  W.,  428 
Maximum  amplitude  with  close  coupling, 

92,  93 

with  loose  coupling,  86,  87 
Measuring  circuit,  107  et  seq.,  119,  124 
Mechanical      quenching,      mechanically 

quenched  gap,  182,  204  et  seq. 
resonance,  330  et  seq. 
MEISSNER,     A.,     Compass,     Telefunken 

radio,  368  et  seq. 

Eddy  currents  in  insulating  mate- 
rials, 409 
Quenched     gap     transmitter     with 

auxiliary  ignition,  377,  378 
Testing  of  coils,  113 
Mercury  arc  lamp  used  as  quenched  gap, 

95,  123 

'turbine  interrupter,  124,  194,  195 
Metallic  granular  coherer,  276,  298,  300 
Microphone  contact,  279 

for  radio -telephony,  373  et  seq. 
Mirror  for  directive  transmission,  340 
rotating,    for    photographing    spark 

image,  3 

MOELLER,  H.  G.,  411 
MONASCH,  B.,   Dissipation  of  energy  in 

condensers,  409 

and  H.  RAUSCH  VON  TRAUBENBERG, 
measurements  with   undamped 
oscillations,  416 
MONCKTON,  C.  C.  F.,  419 
MONTEL,  A.,  410 

MOSCICKI  condensers,  56,  179,  412 
MOSLER,  H.,  Day  and  night  transmission 

compared,  422 
Radio  communication  with  air  ships, 

418 

Receiver  connections,  425 
Mountains,  effect  of,  on  wave  propaga- 
tion, 258  et  seq. 
MUIRHEAD,  A.     See  Lodge. 
MULLER,  C.,  Breakdown  potential  and 

gap  length,  400,  412 
Multiple  antennae,  151,  341  et  seq. 
spark  gap,  20,  98 
tuning  apparatus,  311 


438 


INDEX 


Multiplex  radio-telegraphy,  324  et  seq. 
Multitone  transmitter,  229  et  seq. 


N 


Oscillograph,  4 
OUDIN'S  resonator,  175 
Overloading  detectors,  301 


NASMYTH,  G.  W.,  421 
NATIONAL    ELECTRIC    SIGNALING     Co., 
Brant  Rock,  station  at,  152,  165 
Compressed     air  .  condensers,     55, 

179 

Detectors,  273,  281 
Rotating  spark  gap,  204 
Secrecy  of  messages,  323,  324,  330 
Natural    oscillations  of    condenser    cir- 
cuits, 1  et  seq. 
of  inductive  coils,  33 
of  open  oscillators,  antennae,  24  et 

seq.,  85  et  seq.,  164  et  seq. 
Nauen,  station  at,  64,  152,  155,  158,  168, 

179,  193,  198 
NERNST,  W.,  Electrolytic  detector,  280 

Resistances,  199 
NESPER,  E.,  Detectors,  423 

Frequency    and    damping    meters, 

417 

Impulse  excitation,  182 
Marconi  stations,  419 
Radio  apparatus,  412 
Receiver  connections,  425 
NICHOLSON,  J.  W.,  Effect  of  earth's  cur- 
vature   on    wave    propagation, 
255 

Effective  resistance  of  coils,  411 
Node  of  current  and  of  potential,  25 

NORDMEYER,   P.,  409 


Open  oscillators,  24  et  seq. 

field  of,  35  et  seq. 

general  properties  of,  34  et  seq. 

grounding  of,  46,  157  et  seq. 

with  condensers,  43,  46 

with  end  capacity,  41  et  seq. 

with  inductive  coils,  45 
Orientation  by  means  of  radio-telegraphy, 

367  et  seq. 
ORT,  K,  408 
Oscillation  curves,  2,  389  et  seq. 

valve,  284 
Oscillators,  lineal,  24  et  seq. 

open,  24  el  seq. 


PAPALEXI,     N.    and    L.     MANDELSTAM, 
Dynamometer    effect    and    its 
application,  132  et  seq. 
Production    of    any    desired    phase 

difference,  353  et  seq. 
Parallel,  condensers  in,  6  et  seq. 

resistance  method,  78 
Partial  discharge  sparks,  69 
PAUL,  ROBERT  W.,  Galvanometer,  73 

Interrupter,  183 
PEDERSEN,  P.  O.,  Frequency  of  Poulsen 

transmitter,  421 
Radio-telephony,  426 
Rapid  telegraphy,  229,  302,  323,  337 
Signaling  device  for  Poulsen  trans- 
mitter, 228 
PELLIN,  F.,  427 
PERI,  125,  412 
Perikon  detector,  282,  287 
Period  of  a  condenser  circuit,  natural,  5 

et  seq. 

PETERSEN,  W.,  409 
PETIT,  G.  E.,  352 

PEUCKERT,  W.,  Magnetic  detector,  275 
Quenched  gap  transmitter,  122,  192 
Phase  displacement,  method  of  securing 

any  desired,  352  et  seq. 
Photographic  recorder,  295 
PHYSIKALISCH-TECHNISCHE     REICHSANS- 

TALT,  Poulsen  arc,  226 
PICHON,  P.,  Blower  for  quenched  spark 

gap,  187 

PICKARD,  G.  H.,  Detectors,  273,  282,  423 
PIERCE,  G.  W.,  Detectors,  282,  423 

Investigation  of,  281,  283 
Mercury  arc  lamp  used  as  spark  gap, 

416 
"Principles  of  Wireless  Telegraphy," 

408 

Plate  condensers,  54 
Plates  or  discs,  gap,  187  et  seq. 
POINCARE,  H.,  255 

Polar  lights,  effect  of,  on  wave  propaga- 
tion, 264 

Potential,  anti-node  of,  25 
distribution  curve  of,  25 
node  of,  25 


INDEX 


439 


Potentiometer,  290 

POULSEN,  V.,  Arc  method  of  generating 
undamped    oscillations,    220    et 
seq. 
Interrupter  in  the  receiver,   231   et 

seq.,  420 

Radio -telephony,  371,  374  et  seq. 
Ticker,  334  et  seq. 
Tone  transmitter,  427 
Transmitters,   commercial  form   of, 

222  et  seq. 

Propagation  of  waves  along  earth's  sur- 
face, 246  et  seq. 
velocity  of,  26,  255 
Pulsations  obtained  with  close  coupling, 

89,  95  et  seq. 

tone  reception  by  means  of,  335 
transmission  by  means  of,  378 


Quadrant  electrometer  for  energy  deter- 
mination, 201 

Quasi-stationary  current,  25 
Quenched  spark,  93 

gap,  95  et  seq.,  186  et  seq. 

circuit  used  for  measuring  pur- 
poses, 120,  122,  182 
transmitter,  173,  182  et  seq.,  198 
Quenching  action,  93,  148  et  seq. 
mechanical,  182,  206 
tube,  95 


11 


Radiation,  31,  39  et  seq. 

decrement  of  antennae,  167  et  seq. 
of  condenser  circuits,  11 
of  lineal  oscillators,  31 
resistance  of  antennae,  169  et  seq.,  382 

of  open  oscillators,  40 
Radio-goniometer,  350,  367  et  seq. 
Rain,  effect  of,  on  wave  propagation,  260 

et  seq. 

Range  of  transmission,  271,  305,  314 
Rapid  telegraph  apparatus,  203,  229,  302 
RASCH,  E.,  428 
RAU,    H.,    Experiments   with    quenched 

spark  gaps,  96,  187,  417 
Photographing     spark     in     coupled 

circuits,  89,  95 
RAUTENKRANZ,  J.,  413 
RAYLEIGH,  LORD,  393 


Receiver,  receiving  circuits,  general,  303 

et  seq. 

for  double  wave  transmitter,  177,  314 
for  radio  telephony,  374  ei  seq. 
for  tuned  telegraphy,  310  et  seq. 
for  undamped  oscillations,  332  et  seq. 
Reception  of  signals,  methods  of  recep- 
tion, 290  et  seq. 
Recombination  of  ions,  97 
Recorder,  recording  receiver,  167  et  seq., 

302 

Rectifier,  rectifying  action,  283,  286,  288 
cell    used    for    frequency    transfor- 
mation, 379 
Reflection  of  electromagnetic  waves,  262, 

263 

Reflector  for  directing  waves,  340 
REICH,    M.,    Ground   resistance,   ground 

currents,  417 

Radiation  resistance  of  antennae,  170 
and  H.  TH.  SIMON,  Arc  method,  420 
Reignition  in  oscillating  arc,  236 
REIN,  H.,  "  Radiotelegraphisches  Prakti- 

kum,"  408 

Vieltonsender    (multitone   transmit- 
ter), 420 

Relays,  296  et  seq. 
Reliability  of  detectors,  300,  301 
REMPP,  G.,   Metereological  experiments 

with  radio-telegraphy,  427 
Spark-gap  decrement,  409 
RENDAHL,  R.,  Mercury  arc  lamp  used  as 

quenched  spark  gap,  95 
Variometer,  54 

Resistance,  effective,  12,  47  et  seq.,  396 
equivalent,  85,  120 
of  coils,  50  et  seq. 

of  open  oscillators  antennae,  41,  169 
wires,  398 
Resonance,  85 

curve  of  the  current  effect,  104  et  seq. 
of  the  dynamometer  effect,  132  et 

seq. 

of  the  receiver,  316 
curves,  abnormal  forms  of  the,  116  et 

seq. 

inductor,  coil,  124,  196 
method  for  determining  the  decre- 
ment, 113  et  seq.,  135 
the  frequency,  106  et  seq.,  134 
the  spark-gap  decrement,  16 
sharpness,  105,  405 
transformer,  196 


440 


INDEX 


Responder,  279,  280 

Resultant  capacity,  6  et  seq. 

Retardation  of  discharge,  65,  208 

Rheostat  for  high  frequency  currents,  412 

RICHARDSON,  H.  W.,  and  J.  A.  FLEMING, 
416 

RICHARZ,  F.,  and  W.  ZIEGLER,  408 

RICHTER,  C.,  409 

RIECKE,  E.,  420 

RIEGGER,    H.,    Effect   of   spark   on   fre- 
quency and  resonance  curve,  9, 
416 
Experiments   with   quenched   spark 

gaps,  97,  147,  148 
Theory  of  the  receiver,  321 

Ring  coil,  52 

Rivers,  effect  of,  on  wave  propagation, 
262 

ROGER,  E.,  and  F.  DUCRETET,  Conden- 
sers, 179 
Rotating  spark  gap,  204 

ROHM  ANN,  H.,  Application  of  resonance 
curve  of  the  dynamometer  ef- 
fect, 417 

Experiments  with  quenched  sparks, 
415 

ROSA,  E.  B.,  393 

and  F.  W.  GROVER,  411 

ROSCHANSKY,  D.,  Amplitude  curve  for 
condenser  circuits  with  spark 
gap,  14 

Sequence   of  variations   of  the  gap 
potential,  15,  392 

Rossi,  A.  S.,  275 

Rotating  spark  gaps,  196,  203  et  seq. 

ROUND,  H.  J.,  422 

RUDENBERG,  R.,  High  frequency  ma- 
chine, 420 

Radiation  resistance  of  open  oscil- 
lators or  antennae,  40 
Theory  of  the  receiver,  306 

RUHMER,  E.,  426 

Rupture  of  spark,  16,  117,  124,  206 

RUSCH,  E.,  419 

RUSSEL,  J.,  423 


SACHS,  S.,  423 

Safety  factor  for  commercial  service,  271 
SCHAPIRA,  C.,  420 

SCHELLER,  O..  Call  signal  for  radio-tele- 
phone work,  427 


SCHELLER,  O.,  Fly-wheel  connection,  420 

Quenched  spark  gap,  192 
SCHLOEMILCH,  W.,  Detectois,  273,  277, 

280,  301 

SCHMIDT,  H.,  421 

SCHMIDT,  K.  E.  F.,  Bolometer,  413 
Directive  antennae,  426 
Spark  gap  damping,  409 
SCHWARZHAUPT,     P.,    Atmospheric    dis- 
turbances, 425 

Experiences  as  to  range   of  opera- 
tion, 422 

Screening  to   secure  directive  transmis- 
sion, attempts  at,  340  et  seq. 
Sea  water,  propagation  of  waves  over,  246 

et  seq. 
Secrecy  of  messages,  323  et  seq.,  328  et 

seq.,  336,  365  et  seq. 
sender,  323  et  seq. 
SEIBT,  G.,  Adjustable  condenser,  60 

Connections  for  quenched  gap  trans- 
mitter, 418 

Oscillations  of  coils,  409 
Radio-telephony,  427 
Resonance  inductor,  415 
Variometer,  53 
Zero    method    for    determining    the 

frequency,  416 

Self-induction,  adjustable,  51  et  seq. 
coefficient  of,  47 
effective  coefficient  of,  48 
equations  for  coefficient  of,  393 
measurement  of   coefficient   of,   for 
open  oscillators  or  antennae,  112 
et  seq. 
unit  of,  6 
Sensitiveness  of  detectors  and  ticker,  289 

et  seq.,  300  et  seq.,  334 
Series  connection  of  condensers,  6  et  seq. 

spark  gap,  20,  98,  189 
Ship  antennae,  153  et  seq.,  165,  168 
SHOEMAKER,  H.,  427 
Short-circuit  loop  dynamometer,  136 

spark  gap,  207 
SIEWERT,  417 
SIMON,  H.,  424 
SIMON,  H.  TH.,  Arc,  characteristics  of  the, 

428 

generator,  222 
method  for  producing  undamped 

oscillations,  231,  420 
Mercury  arc  lamp  used  as  spark  gap, 


INDEX 


441 


SIMON,    H,    TH.,    and    M.    REICH,    Arc 

method,  420 
SIMONS,  K.,  409 
Simple  antennae,  150,  169 
Siphon  recorder,  294 
Skin  effect,  47 
SLABY,  A.,  Coupled  circuits,  414 

Receiver  for  tuned  oscillations,  313 
Societe  frangaise  radioelectrique,  419 
SOLPP,  K.,  Data  on  antennas,  417 

Radio  communication  with  airships, 

418 
SOMMERFELD,  A.,  Coilsfor  high  frequency , 

411 
Propagation      of      electromagnetic 

waves,  248  et  seq.,  421 
Sound  intensifier,  291  et  seq.,  297,  331 
Source  of  energy  supplied  to  radio  trans- 
mitters, 199  et  seq. 
Space  waves,  249 
Spark,  1 

constants,  14,  392 
damping,  15 

effect  of  the,  on  the  frequency,  9 
gap,  1,  180 
decrement,  15 
micrometer,  66 
quenched.     See  Quenched. 
resistance,  15 

with  rotating  electrodes,  203  et  seq. 
potential,  14,  392 
the  term,  compared  with  arc,  245 
Speed  of  telegraphing,  302 
SQUIER,  O.,  303,  424 
"Static."     See  Atmospheric  disturbances 

characteristic  of  the  arc,  231 
Station  tester,  183 
Stationary  waves,  26 
STEINHAUS,  W.,  413 
STONE,  J.  ST.,  Directive  antennas,  345 
•Receivers  having  several  condenser 

circuits,  425 

Theory  of  coupled  circuits,  415 
STRASSER,  B.,  393 
Stray  energy  coefficient,  257 
Straying  of  energy  along  earth's  surface, 

256 

String  galvanometer,  296 
STUFF,  W.,  408 
SUBKIS,  S.,  101,  239 
Substitution    method    for    determining 

spark-gap  resistance,  16  et  seq. 
Sunlight.     See  Daylight. 


Supply  circuit,  199  et  seq. 
Surface  waves,  249 
SUTTON,  H.,  423 
SZIVESSY,  G.,  416 


TALSCH,  E.,  415 

Tapper,  298 

TAYLOR,  J.  E.,  Atmospheric  disturbances, 

425 

Telephonic  reception,  424 
and  W.  DUDDELL,  260,  269,  272,  273 
TELEFUNKEN.     See  Gesellschaft  fur  draht- 

lose  Telegraphic. 
compass, 

Telephone  relay,  291  et  seq.,  374 
Telephonic    reception  of    radio    signals, 

290  et  seq. 

Telephony,  wireless,  370  et  seq. 
TESLA,  N.,  Arc  method,  123 

Braided  wires,  49 
Thermal  detectors,  wave  detectors,  273 

et  seq. 

galvanometer,  75  et  seq.,  77,  272 
Thermocouple  thermoelement,  74  et  seq., 

77,  273 

THORNBLAD,  TH.  G.,  417 
THOMSON,  EL.,  Arc  method,  220 
THOMSON'S    (Sm   WM.)    equation,   5,   8, 

408 

Ticker,  334  ei  seq. 

TISSOT,  C.,  Bolometer,  72,  272,  413,  422 
Experiments  on  wave  propagation^ 

269,  422 
Investigation    of    detectors,    282    et 

seq.,  423 
Longitude  determination  by  means 

of  radio  signals,  427 
Radio  telephony,  427 

time  signals,  427 

Rheostat   for   high   frequency   cur- 
rents, 412 
TOEPLER,  M.,  412 

Tone  intensifier.     See  Sound  intensifier. 
reception,  378 
transmitter,  195,  198,  206,  230,  292, 

297,  325,  328,  330,  377 
Tosi,  A.,  and  E.  BELLINI,  347  et  seq.,  367 
Transformation  of  frequency,  379 
Transmitter  of  Braun,  173,  175  et  seq. 
of  Marconi  (simple),  173  et  seq. 
of  Wien,  173,  182  et  seq.,  209  et  seq. 


442 


INDEX 


TRAUBENBERG,  H.  RAUSCH  VON,  Poulsen 

generator,  222 
Spark-gap  resistance,  409 
and    B.    MONASCH,    Measurements 
with  undamped  oscillations,  416 
Trees  used  as  receiving  antennae,  303 
Triplex  reception  with  one  antenna,  425 
TRUE,  H.,  158,  163 

Tuned  telegraphy,  310  et  seq.,  328  et  seq. 
Tuning,  85,  314 

coils  for,  166,  316,  382 
condensers  for,  167 
sharpness  of,  314,  316  et  seq. 
Turbine  interrupter,  mercury,  124,  194, 

195 

TURPAIN,  A.,  422 

Two-wave  transmitter,  receiver  for,  176 
et  seq.,  314  et  seq. 


U 


ULLER,     K.,     Specific    conductivity    of 

various  materials,  421 
Wave    propagation     along     earth's 

surface,  421 

Umbrella  antennae,  152,  169 
Undamped  oscillations,  2 

as  used  for    measuring    purposes, 

116,  119,  121,  225 
generated  by  alternating  current 

machines,  213  et  seq. 
by  the  arc  method,  220  et  seq. 
receivers  for,  332  et  seq. 
Unilateral  transmitter  for  directive  te- 
legraphy, 345 

Untuned  circuits,  coupling  of,  147 
Upper    harmonic    oscillations    of    lineal 

oscillators,  24  et  seq.,  32 
of  open  oscillators,  24  et  seq. 
UPSON,  W.  L.,  428 


Variometer,  53,  192 

Vector  diagram  applied  to  field  of  dou- 
ble transmitter,  284  et  seq.,  286,  288, 
342 

Velocity  of  wave  propagation,  26,  255 

Vieltonsender .    See  Multitone  transmitter . 

VOEGE,  77 

VOIGT,  E.,  412 

VOLLMER,  K.,  241 


W 


WAGNER,  K.  W.,  421 
WALTER,  L.  H.,  Detectors,  275,  279 
Distance  effect  characteristics,  425 
Experiments  with  Peuckert's  genera- 
tor, 419 

WARBURG,  E.,  65 
WASMUS,  A.,  Determination  of  discharge 

frequency,  413 

Experiments   with    Peuckert's  gen- 
erator, 419 
Water,     stream     of,    used    as    antenna, 

150 

WATSON,  E.  A.,  412 
Wattmeter  for  measuring  energy,  201 

hot-wire,  71 

Wave  indicators,  272  et  seq. 
length,  26 

of  condenser  circuits,  386 

and  corresponding  frequency,  388 

relation  of,  to  propagation,  251, 

265  et  seq.,  381 
Wavemeters,  125  et  seq. 
Waves,  advancing,  26,  29 

propagation  of,  along  earth's  surface, 

246  et  seq. 
stationary,  26 

Weather,  effects  of  the,  168,  263  et  seq. 
WEHNELT,  A.,  284,  424 
WEICKER,  W.,  400 
WEISS,  P.,  423 
WERTHEIM-SALOMONSON,  221 
WHEATSTONE  rapid  telegraph  apparatus, 

203 

WIEN,  M.,  Acoustic  resonance,  425 
Effect  of  spark  on  the  frequency,  9 
Efficiency  of  coupled  transmitters, 

211 
Experiments  with  coupled  circuits, 

142,  147,  415 
Investigation  of  condensers,  57,  140, 

409,  412 
Loose  coupling,  87,  414 

for  tuned  telegraphy,  322 
Quenched  gap  transmitter,  93  et  seq., 

182  et  seq.,  208  et  seq. 
Quenching  tubes,  95 
Resonance  curves,  416 
Spark-gap  decrement,  18 
WILDMANN,  422 
WILSON,  E.,  423 
WOLF,  M.,  412 


INDEX 


443 


ZEBRIKOFF,  L.,  and  C.  E.  GUYE,  392 
ZEHNDER,  L.,   Effect  of  atmosphere  on 

the  waves,  422 
Ground  antennae,  364 
ZENNECK,    J.,   Action    of  bent  Marconi 

antenna  when  receiving,  361 
Amplitude   curve  of   condenser   cir- 
cuits with  spark  gap,  13 
Direct  coupling,  414 


ZENNECK,  J.,  Experiments  with  coupled 

circuits,  93,  142  et  seq. 
with  directive  telegraphy,  340 
Field   of   electromagnetic  waves   at 

the  earth's  surface,  252 
Frequency      transformation,      379, 

380 

Wavemeter,  127 

ZIEGLER,  W.,  and  F.  RICHARZ,  408 
ZOLLICH,  H.,  413 
ZORN,  W.,  409 


desk  from  which  borrowed. 


LD2l-100m-9,'48(B399sl6)476 


YC   19348 


373881 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


mi  • 


